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Simplifying 0.5x(2x + -9) = 90 Reorder the terms: 0.5x(-9 + 2x) = 90 (-9 * 0.5x + 2x * 0.5x) = 90 (-4.5x + 1x2) = 90 Solving -4.5x + 1x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -4.5x + 1x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -4.5x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -4.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -4.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -4.5x + x2 = 0 + 90 -4.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -4.5x + x2 = 90 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 90 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 90 + 5.0625 Combine like terms: 90 + 5.0625 = 95.0625 5.0625 + -4.5x + x2 = 95.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 95.0625 Calculate the square root of the right side: 9.75 Break this problem into two subproblems by setting (x + -2.25) equal to 9.75 and -9.75.Subproblem 1
x + -2.25 = 9.75 Simplifying x + -2.25 = 9.75 Reorder the terms: -2.25 + x = 9.75 Solving -2.25 + x = 9.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 9.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 9.75 + 2.25 x = 9.75 + 2.25 Combine like terms: 9.75 + 2.25 = 12 x = 12 Simplifying x = 12Subproblem 2
x + -2.25 = -9.75 Simplifying x + -2.25 = -9.75 Reorder the terms: -2.25 + x = -9.75 Solving -2.25 + x = -9.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -9.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -9.75 + 2.25 x = -9.75 + 2.25 Combine like terms: -9.75 + 2.25 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, -7.5}
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