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Simplifying 90 + (3x + 5) * x + 2x = 180 Reorder the terms: 90 + (5 + 3x) * x + 2x = 180 Reorder the terms for easier multiplication: 90 + x(5 + 3x) + 2x = 180 90 + (5 * x + 3x * x) + 2x = 180 90 + (5x + 3x2) + 2x = 180 Reorder the terms: 90 + 5x + 2x + 3x2 = 180 Combine like terms: 5x + 2x = 7x 90 + 7x + 3x2 = 180 Solving 90 + 7x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 90 + -180 + 7x + 3x2 = 180 + -180 Combine like terms: 90 + -180 = -90 -90 + 7x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -90 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 2.333333333x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 2.333333333x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2.333333333x + x2 = 0 + 30 2.333333333x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 2.333333333x + x2 = 30 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 30 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 30 + 1.361111112 Combine like terms: 30 + 1.361111112 = 31.361111112 1.361111112 + 2.333333333x + x2 = 31.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 31.361111112 Calculate the square root of the right side: 5.600099206 Break this problem into two subproblems by setting (x + 1.166666667) equal to 5.600099206 and -5.600099206.Subproblem 1
x + 1.166666667 = 5.600099206 Simplifying x + 1.166666667 = 5.600099206 Reorder the terms: 1.166666667 + x = 5.600099206 Solving 1.166666667 + x = 5.600099206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 5.600099206 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 5.600099206 + -1.166666667 x = 5.600099206 + -1.166666667 Combine like terms: 5.600099206 + -1.166666667 = 4.433432539 x = 4.433432539 Simplifying x = 4.433432539Subproblem 2
x + 1.166666667 = -5.600099206 Simplifying x + 1.166666667 = -5.600099206 Reorder the terms: 1.166666667 + x = -5.600099206 Solving 1.166666667 + x = -5.600099206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -5.600099206 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -5.600099206 + -1.166666667 x = -5.600099206 + -1.166666667 Combine like terms: -5.600099206 + -1.166666667 = -6.766765873 x = -6.766765873 Simplifying x = -6.766765873Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.433432539, -6.766765873}
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