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Simplifying 0 = 2x2 + -15x + 15 Reorder the terms: 0 = 15 + -15x + 2x2 Solving 0 = 15 + -15x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + 15x + -2x2 = 15 + -15x + 2x2 + -15 + 15x + -2x2 Reorder the terms: -15 + 15x + -2x2 = 15 + -15 + -15x + 15x + 2x2 + -2x2 Combine like terms: 15 + -15 = 0 -15 + 15x + -2x2 = 0 + -15x + 15x + 2x2 + -2x2 -15 + 15x + -2x2 = -15x + 15x + 2x2 + -2x2 Combine like terms: -15x + 15x = 0 -15 + 15x + -2x2 = 0 + 2x2 + -2x2 -15 + 15x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7.5x + x2 = 0 + -7.5 -7.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7.5x + x2 = -7.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -7.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -7.5 + 14.0625 Combine like terms: -7.5 + 14.0625 = 6.5625 14.0625 + -7.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -3.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + -3.75 = 2.561737691 Simplifying x + -3.75 = 2.561737691 Reorder the terms: -3.75 + x = 2.561737691 Solving -3.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 2.561737691 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.561737691 + 3.75 x = 2.561737691 + 3.75 Combine like terms: 2.561737691 + 3.75 = 6.311737691 x = 6.311737691 Simplifying x = 6.311737691Subproblem 2
x + -3.75 = -2.561737691 Simplifying x + -3.75 = -2.561737691 Reorder the terms: -3.75 + x = -2.561737691 Solving -3.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -2.561737691 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.561737691 + 3.75 x = -2.561737691 + 3.75 Combine like terms: -2.561737691 + 3.75 = 1.188262309 x = 1.188262309 Simplifying x = 1.188262309Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.311737691, 1.188262309}
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