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Simplifying x * x + -12x + 15 = 3x + -5 Multiply x * x x2 + -12x + 15 = 3x + -5 Reorder the terms: 15 + -12x + x2 = 3x + -5 Reorder the terms: 15 + -12x + x2 = -5 + 3x Solving 15 + -12x + x2 = -5 + 3x Solving for variable 'x'. Reorder the terms: 15 + 5 + -12x + -3x + x2 = -5 + 3x + 5 + -3x Combine like terms: 15 + 5 = 20 20 + -12x + -3x + x2 = -5 + 3x + 5 + -3x Combine like terms: -12x + -3x = -15x 20 + -15x + x2 = -5 + 3x + 5 + -3x Reorder the terms: 20 + -15x + x2 = -5 + 5 + 3x + -3x Combine like terms: -5 + 5 = 0 20 + -15x + x2 = 0 + 3x + -3x 20 + -15x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 20 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -15x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -15x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -15x + x2 = 0 + -20 -15x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -15x + x2 = -20 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -20 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -20 + 56.25 Combine like terms: -20 + 56.25 = 36.25 56.25 + -15x + x2 = 36.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -7.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -7.5 = 6.020797289 Simplifying x + -7.5 = 6.020797289 Reorder the terms: -7.5 + x = 6.020797289 Solving -7.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.020797289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.020797289 + 7.5 x = 6.020797289 + 7.5 Combine like terms: 6.020797289 + 7.5 = 13.520797289 x = 13.520797289 Simplifying x = 13.520797289Subproblem 2
x + -7.5 = -6.020797289 Simplifying x + -7.5 = -6.020797289 Reorder the terms: -7.5 + x = -6.020797289 Solving -7.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.020797289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.020797289 + 7.5 x = -6.020797289 + 7.5 Combine like terms: -6.020797289 + 7.5 = 1.479202711 x = 1.479202711 Simplifying x = 1.479202711Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.520797289, 1.479202711}
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