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Simplifying 7x2 + 14x + -10 = 112634 Reorder the terms: -10 + 14x + 7x2 = 112634 Solving -10 + 14x + 7x2 = 112634 Solving for variable 'x'. Reorder the terms: -10 + -112634 + 14x + 7x2 = 112634 + -112634 Combine like terms: -10 + -112634 = -112644 -112644 + 14x + 7x2 = 112634 + -112634 Combine like terms: 112634 + -112634 = 0 -112644 + 14x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-16092 + 2x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-16092 + 2x + x2)' equal to zero and attempt to solve: Simplifying -16092 + 2x + x2 = 0 Solving -16092 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16092' to each side of the equation. -16092 + 2x + 16092 + x2 = 0 + 16092 Reorder the terms: -16092 + 16092 + 2x + x2 = 0 + 16092 Combine like terms: -16092 + 16092 = 0 0 + 2x + x2 = 0 + 16092 2x + x2 = 0 + 16092 Combine like terms: 0 + 16092 = 16092 2x + x2 = 16092 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 16092 + 1 Reorder the terms: 1 + 2x + x2 = 16092 + 1 Combine like terms: 16092 + 1 = 16093 1 + 2x + x2 = 16093 Factor a perfect square on the left side: (x + 1)(x + 1) = 16093 Calculate the square root of the right side: 126.858188541 Break this problem into two subproblems by setting (x + 1) equal to 126.858188541 and -126.858188541.Subproblem 1
x + 1 = 126.858188541 Simplifying x + 1 = 126.858188541 Reorder the terms: 1 + x = 126.858188541 Solving 1 + x = 126.858188541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 126.858188541 + -1 Combine like terms: 1 + -1 = 0 0 + x = 126.858188541 + -1 x = 126.858188541 + -1 Combine like terms: 126.858188541 + -1 = 125.858188541 x = 125.858188541 Simplifying x = 125.858188541Subproblem 2
x + 1 = -126.858188541 Simplifying x + 1 = -126.858188541 Reorder the terms: 1 + x = -126.858188541 Solving 1 + x = -126.858188541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -126.858188541 + -1 Combine like terms: 1 + -1 = 0 0 + x = -126.858188541 + -1 x = -126.858188541 + -1 Combine like terms: -126.858188541 + -1 = -127.858188541 x = -127.858188541 Simplifying x = -127.858188541Solution
The solution to the problem is based on the solutions from the subproblems. x = {125.858188541, -127.858188541}Solution
x = {125.858188541, -127.858188541}
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