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Simplifying (x2) + 8x + 15 = -1(7x) + 21 x2 + 8x + 15 = -1(7x) + 21 Reorder the terms: 15 + 8x + x2 = -1(7x) + 21 Remove parenthesis around (7x) 15 + 8x + x2 = -1 * 7x + 21 Multiply -1 * 7 15 + 8x + x2 = -7x + 21 Reorder the terms: 15 + 8x + x2 = 21 + -7x Solving 15 + 8x + x2 = 21 + -7x Solving for variable 'x'. Reorder the terms: 15 + -21 + 8x + 7x + x2 = 21 + -7x + -21 + 7x Combine like terms: 15 + -21 = -6 -6 + 8x + 7x + x2 = 21 + -7x + -21 + 7x Combine like terms: 8x + 7x = 15x -6 + 15x + x2 = 21 + -7x + -21 + 7x Reorder the terms: -6 + 15x + x2 = 21 + -21 + -7x + 7x Combine like terms: 21 + -21 = 0 -6 + 15x + x2 = 0 + -7x + 7x -6 + 15x + x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -6 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 15x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 15x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 15x + x2 = 0 + 6 15x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 15x + x2 = 6 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 = 6 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 6 + 56.25 Combine like terms: 6 + 56.25 = 62.25 56.25 + 15x + x2 = 62.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 7.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 7.5 = 7.889866919 Simplifying x + 7.5 = 7.889866919 Reorder the terms: 7.5 + x = 7.889866919 Solving 7.5 + x = 7.889866919 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 = 7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.889866919 + -7.5 x = 7.889866919 + -7.5 Combine like terms: 7.889866919 + -7.5 = 0.389866919 x = 0.389866919 Simplifying x = 0.389866919Subproblem 2
x + 7.5 = -7.889866919 Simplifying x + 7.5 = -7.889866919 Reorder the terms: 7.5 + x = -7.889866919 Solving 7.5 + x = -7.889866919 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 = -7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.889866919 + -7.5 x = -7.889866919 + -7.5 Combine like terms: -7.889866919 + -7.5 = -15.389866919 x = -15.389866919 Simplifying x = -15.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.389866919, -15.389866919}
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