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Simplifying 4x2 + 56x + -180 = 0 Reorder the terms: -180 + 56x + 4x2 = 0 Solving -180 + 56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 14x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 14x + x2)' equal to zero and attempt to solve: Simplifying -45 + 14x + x2 = 0 Solving -45 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 14x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 14x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 14x + x2 = 0 + 45 14x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 14x + x2 = 45 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 = 45 + 49 Reorder the terms: 49 + 14x + x2 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + 14x + x2 = 94 Factor a perfect square on the left side: (x + 7)(x + 7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 7) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 7 = 9.695359715 Simplifying x + 7 = 9.695359715 Reorder the terms: 7 + x = 9.695359715 Solving 7 + x = 9.695359715 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 = 9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.695359715 + -7 x = 9.695359715 + -7 Combine like terms: 9.695359715 + -7 = 2.695359715 x = 2.695359715 Simplifying x = 2.695359715Subproblem 2
x + 7 = -9.695359715 Simplifying x + 7 = -9.695359715 Reorder the terms: 7 + x = -9.695359715 Solving 7 + x = -9.695359715 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 = -9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.695359715 + -7 x = -9.695359715 + -7 Combine like terms: -9.695359715 + -7 = -16.695359715 x = -16.695359715 Simplifying x = -16.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.695359715, -16.695359715}Solution
x = {2.695359715, -16.695359715}
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