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Simplifying 5x2 + 340x + -1020 = 0 Reorder the terms: -1020 + 340x + 5x2 = 0 Solving -1020 + 340x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-204 + 68x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-204 + 68x + x2)' equal to zero and attempt to solve: Simplifying -204 + 68x + x2 = 0 Solving -204 + 68x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + 68x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 68x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 68x + x2 = 0 + 204 68x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 68x + x2 = 204 The x term is 68x. Take half its coefficient (34). Square it (1156) and add it to both sides. Add '1156' to each side of the equation. 68x + 1156 + x2 = 204 + 1156 Reorder the terms: 1156 + 68x + x2 = 204 + 1156 Combine like terms: 204 + 1156 = 1360 1156 + 68x + x2 = 1360 Factor a perfect square on the left side: (x + 34)(x + 34) = 1360 Calculate the square root of the right side: 36.878177829 Break this problem into two subproblems by setting (x + 34) equal to 36.878177829 and -36.878177829.Subproblem 1
x + 34 = 36.878177829 Simplifying x + 34 = 36.878177829 Reorder the terms: 34 + x = 36.878177829 Solving 34 + x = 36.878177829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + x = 36.878177829 + -34 Combine like terms: 34 + -34 = 0 0 + x = 36.878177829 + -34 x = 36.878177829 + -34 Combine like terms: 36.878177829 + -34 = 2.878177829 x = 2.878177829 Simplifying x = 2.878177829Subproblem 2
x + 34 = -36.878177829 Simplifying x + 34 = -36.878177829 Reorder the terms: 34 + x = -36.878177829 Solving 34 + x = -36.878177829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + x = -36.878177829 + -34 Combine like terms: 34 + -34 = 0 0 + x = -36.878177829 + -34 x = -36.878177829 + -34 Combine like terms: -36.878177829 + -34 = -70.878177829 x = -70.878177829 Simplifying x = -70.878177829Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.878177829, -70.878177829}Solution
x = {2.878177829, -70.878177829}
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