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Simplifying 90 = x * x + 3x Multiply x * x 90 = x2 + 3x Reorder the terms: 90 = 3x + x2 Solving 90 = 3x + x2 Solving for variable 'x'. Reorder the terms: 90 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 90 + -3x + -1x2 = 0 + x2 + -1x2 90 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 90 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + 3x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 3x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 3x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 3x + x2 = 0 + 90 3x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 3x + x2 = 90 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 90 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 90 + 2.25 Combine like terms: 90 + 2.25 = 92.25 2.25 + 3x + x2 = 92.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + 1.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + 1.5 = 9.604686356 Simplifying x + 1.5 = 9.604686356 Reorder the terms: 1.5 + x = 9.604686356 Solving 1.5 + x = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.604686356 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.604686356 + -1.5 x = 9.604686356 + -1.5 Combine like terms: 9.604686356 + -1.5 = 8.104686356 x = 8.104686356 Simplifying x = 8.104686356Subproblem 2
x + 1.5 = -9.604686356 Simplifying x + 1.5 = -9.604686356 Reorder the terms: 1.5 + x = -9.604686356 Solving 1.5 + x = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.604686356 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.604686356 + -1.5 x = -9.604686356 + -1.5 Combine like terms: -9.604686356 + -1.5 = -11.104686356 x = -11.104686356 Simplifying x = -11.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.104686356, -11.104686356}
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