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Simplifying 8 = -2x2 + -28x + 90 Reorder the terms: 8 = 90 + -28x + -2x2 Solving 8 = 90 + -28x + -2x2 Solving for variable 'x'. Combine like terms: 8 + -90 = -82 -82 + 28x + 2x2 = 90 + -28x + -2x2 + -90 + 28x + 2x2 Reorder the terms: -82 + 28x + 2x2 = 90 + -90 + -28x + 28x + -2x2 + 2x2 Combine like terms: 90 + -90 = 0 -82 + 28x + 2x2 = 0 + -28x + 28x + -2x2 + 2x2 -82 + 28x + 2x2 = -28x + 28x + -2x2 + 2x2 Combine like terms: -28x + 28x = 0 -82 + 28x + 2x2 = 0 + -2x2 + 2x2 -82 + 28x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -82 + 28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + 14x + x2)' equal to zero and attempt to solve: Simplifying -41 + 14x + x2 = 0 Solving -41 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 14x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 14x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 14x + x2 = 0 + 41 14x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 14x + x2 = 41 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 41 + 49 Reorder the terms: 49 + 14x + x2 = 41 + 49 Combine like terms: 41 + 49 = 90 49 + 14x + x2 = 90 Factor a perfect square on the left side: (x + 7)(x + 7) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 7) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 7 = 9.486832981 Simplifying x + 7 = 9.486832981 Reorder the terms: 7 + x = 9.486832981 Solving 7 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 9.486832981 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.486832981 + -7 x = 9.486832981 + -7 Combine like terms: 9.486832981 + -7 = 2.486832981 x = 2.486832981 Simplifying x = 2.486832981Subproblem 2
x + 7 = -9.486832981 Simplifying x + 7 = -9.486832981 Reorder the terms: 7 + x = -9.486832981 Solving 7 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -9.486832981 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.486832981 + -7 x = -9.486832981 + -7 Combine like terms: -9.486832981 + -7 = -16.486832981 x = -16.486832981 Simplifying x = -16.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.486832981, -16.486832981}Solution
x = {2.486832981, -16.486832981}
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