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Simplifying 2(3x + -7) + 25 = -7(x + -4) * 17x + -17 Reorder the terms: 2(-7 + 3x) + 25 = -7(x + -4) * 17x + -17 (-7 * 2 + 3x * 2) + 25 = -7(x + -4) * 17x + -17 (-14 + 6x) + 25 = -7(x + -4) * 17x + -17 Reorder the terms: -14 + 25 + 6x = -7(x + -4) * 17x + -17 Combine like terms: -14 + 25 = 11 11 + 6x = -7(x + -4) * 17x + -17 Reorder the terms: 11 + 6x = -7(-4 + x) * 17x + -17 Reorder the terms for easier multiplication: 11 + 6x = -7 * 17x(-4 + x) + -17 Multiply -7 * 17 11 + 6x = -119x(-4 + x) + -17 11 + 6x = (-4 * -119x + x * -119x) + -17 11 + 6x = (476x + -119x2) + -17 Reorder the terms: 11 + 6x = -17 + 476x + -119x2 Solving 11 + 6x = -17 + 476x + -119x2 Solving for variable 'x'. Reorder the terms: 11 + 17 + 6x + -476x + 119x2 = -17 + 476x + -119x2 + 17 + -476x + 119x2 Combine like terms: 11 + 17 = 28 28 + 6x + -476x + 119x2 = -17 + 476x + -119x2 + 17 + -476x + 119x2 Combine like terms: 6x + -476x = -470x 28 + -470x + 119x2 = -17 + 476x + -119x2 + 17 + -476x + 119x2 Reorder the terms: 28 + -470x + 119x2 = -17 + 17 + 476x + -476x + -119x2 + 119x2 Combine like terms: -17 + 17 = 0 28 + -470x + 119x2 = 0 + 476x + -476x + -119x2 + 119x2 28 + -470x + 119x2 = 476x + -476x + -119x2 + 119x2 Combine like terms: 476x + -476x = 0 28 + -470x + 119x2 = 0 + -119x2 + 119x2 28 + -470x + 119x2 = -119x2 + 119x2 Combine like terms: -119x2 + 119x2 = 0 28 + -470x + 119x2 = 0 Begin completing the square. Divide all terms by 119 the coefficient of the squared term: Divide each side by '119'. 0.2352941176 + -3.949579832x + x2 = 0 Move the constant term to the right: Add '-0.2352941176' to each side of the equation. 0.2352941176 + -3.949579832x + -0.2352941176 + x2 = 0 + -0.2352941176 Reorder the terms: 0.2352941176 + -0.2352941176 + -3.949579832x + x2 = 0 + -0.2352941176 Combine like terms: 0.2352941176 + -0.2352941176 = 0.0000000000 0.0000000000 + -3.949579832x + x2 = 0 + -0.2352941176 -3.949579832x + x2 = 0 + -0.2352941176 Combine like terms: 0 + -0.2352941176 = -0.2352941176 -3.949579832x + x2 = -0.2352941176 The x term is -3.949579832x. Take half its coefficient (-1.974789916). Square it (3.899795212) and add it to both sides. Add '3.899795212' to each side of the equation. -3.949579832x + 3.899795212 + x2 = -0.2352941176 + 3.899795212 Reorder the terms: 3.899795212 + -3.949579832x + x2 = -0.2352941176 + 3.899795212 Combine like terms: -0.2352941176 + 3.899795212 = 3.6645010944 3.899795212 + -3.949579832x + x2 = 3.6645010944 Factor a perfect square on the left side: (x + -1.974789916)(x + -1.974789916) = 3.6645010944 Calculate the square root of the right side: 1.914288665 Break this problem into two subproblems by setting (x + -1.974789916) equal to 1.914288665 and -1.914288665.Subproblem 1
x + -1.974789916 = 1.914288665 Simplifying x + -1.974789916 = 1.914288665 Reorder the terms: -1.974789916 + x = 1.914288665 Solving -1.974789916 + x = 1.914288665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.974789916' to each side of the equation. -1.974789916 + 1.974789916 + x = 1.914288665 + 1.974789916 Combine like terms: -1.974789916 + 1.974789916 = 0.000000000 0.000000000 + x = 1.914288665 + 1.974789916 x = 1.914288665 + 1.974789916 Combine like terms: 1.914288665 + 1.974789916 = 3.889078581 x = 3.889078581 Simplifying x = 3.889078581Subproblem 2
x + -1.974789916 = -1.914288665 Simplifying x + -1.974789916 = -1.914288665 Reorder the terms: -1.974789916 + x = -1.914288665 Solving -1.974789916 + x = -1.914288665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.974789916' to each side of the equation. -1.974789916 + 1.974789916 + x = -1.914288665 + 1.974789916 Combine like terms: -1.974789916 + 1.974789916 = 0.000000000 0.000000000 + x = -1.914288665 + 1.974789916 x = -1.914288665 + 1.974789916 Combine like terms: -1.914288665 + 1.974789916 = 0.060501251 x = 0.060501251 Simplifying x = 0.060501251Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.889078581, 0.060501251}
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