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Simplifying (4x + -15) * x = 180 Reorder the terms: (-15 + 4x) * x = 180 Reorder the terms for easier multiplication: x(-15 + 4x) = 180 (-15 * x + 4x * x) = 180 (-15x + 4x2) = 180 Solving -15x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -15x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -45 + -3.75x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -3.75x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -3.75x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -3.75x + x2 = 0 + 45 -3.75x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -3.75x + x2 = 45 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 45 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 45 + 3.515625 Combine like terms: 45 + 3.515625 = 48.515625 3.515625 + -3.75x + x2 = 48.515625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 48.515625 Calculate the square root of the right side: 6.965315858 Break this problem into two subproblems by setting (x + -1.875) equal to 6.965315858 and -6.965315858.Subproblem 1
x + -1.875 = 6.965315858 Simplifying x + -1.875 = 6.965315858 Reorder the terms: -1.875 + x = 6.965315858 Solving -1.875 + x = 6.965315858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 6.965315858 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 6.965315858 + 1.875 x = 6.965315858 + 1.875 Combine like terms: 6.965315858 + 1.875 = 8.840315858 x = 8.840315858 Simplifying x = 8.840315858Subproblem 2
x + -1.875 = -6.965315858 Simplifying x + -1.875 = -6.965315858 Reorder the terms: -1.875 + x = -6.965315858 Solving -1.875 + x = -6.965315858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -6.965315858 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -6.965315858 + 1.875 x = -6.965315858 + 1.875 Combine like terms: -6.965315858 + 1.875 = -5.090315858 x = -5.090315858 Simplifying x = -5.090315858Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.840315858, -5.090315858}
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