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Simplifying 3x2 + -4x + 7 = x2 + 15x Reorder the terms: 7 + -4x + 3x2 = x2 + 15x Reorder the terms: 7 + -4x + 3x2 = 15x + x2 Solving 7 + -4x + 3x2 = 15x + x2 Solving for variable 'x'. Reorder the terms: 7 + -4x + -15x + 3x2 + -1x2 = 15x + x2 + -15x + -1x2 Combine like terms: -4x + -15x = -19x 7 + -19x + 3x2 + -1x2 = 15x + x2 + -15x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 7 + -19x + 2x2 = 15x + x2 + -15x + -1x2 Reorder the terms: 7 + -19x + 2x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 7 + -19x + 2x2 = 0 + x2 + -1x2 7 + -19x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -9.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -9.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -9.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -9.5x + x2 = 0 + -3.5 -9.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -9.5x + x2 = -3.5 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -3.5 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -3.5 + 22.5625 Combine like terms: -3.5 + 22.5625 = 19.0625 22.5625 + -9.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + -4.75) equal to 4.366062299 and -4.366062299.Subproblem 1
x + -4.75 = 4.366062299 Simplifying x + -4.75 = 4.366062299 Reorder the terms: -4.75 + x = 4.366062299 Solving -4.75 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 4.366062299 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.366062299 + 4.75 x = 4.366062299 + 4.75 Combine like terms: 4.366062299 + 4.75 = 9.116062299 x = 9.116062299 Simplifying x = 9.116062299Subproblem 2
x + -4.75 = -4.366062299 Simplifying x + -4.75 = -4.366062299 Reorder the terms: -4.75 + x = -4.366062299 Solving -4.75 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -4.366062299 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.366062299 + 4.75 x = -4.366062299 + 4.75 Combine like terms: -4.366062299 + 4.75 = 0.383937701 x = 0.383937701 Simplifying x = 0.383937701Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.116062299, 0.383937701}
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