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Simplifying 57x2 + -84x + -45 = 0 Reorder the terms: -45 + -84x + 57x2 = 0 Solving -45 + -84x + 57x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -28x + 19x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + -28x + 19x2)' equal to zero and attempt to solve: Simplifying -15 + -28x + 19x2 = 0 Solving -15 + -28x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.7894736842 + -1.473684211x + x2 = 0 Move the constant term to the right: Add '0.7894736842' to each side of the equation. -0.7894736842 + -1.473684211x + 0.7894736842 + x2 = 0 + 0.7894736842 Reorder the terms: -0.7894736842 + 0.7894736842 + -1.473684211x + x2 = 0 + 0.7894736842 Combine like terms: -0.7894736842 + 0.7894736842 = 0.0000000000 0.0000000000 + -1.473684211x + x2 = 0 + 0.7894736842 -1.473684211x + x2 = 0 + 0.7894736842 Combine like terms: 0 + 0.7894736842 = 0.7894736842 -1.473684211x + x2 = 0.7894736842 The x term is -1.473684211x. Take half its coefficient (-0.7368421055). Square it (0.5429362884) and add it to both sides. Add '0.5429362884' to each side of the equation. -1.473684211x + 0.5429362884 + x2 = 0.7894736842 + 0.5429362884 Reorder the terms: 0.5429362884 + -1.473684211x + x2 = 0.7894736842 + 0.5429362884 Combine like terms: 0.7894736842 + 0.5429362884 = 1.3324099726 0.5429362884 + -1.473684211x + x2 = 1.3324099726 Factor a perfect square on the left side: (x + -0.7368421055)(x + -0.7368421055) = 1.3324099726 Calculate the square root of the right side: 1.154300642 Break this problem into two subproblems by setting (x + -0.7368421055) equal to 1.154300642 and -1.154300642.Subproblem 1
x + -0.7368421055 = 1.154300642 Simplifying x + -0.7368421055 = 1.154300642 Reorder the terms: -0.7368421055 + x = 1.154300642 Solving -0.7368421055 + x = 1.154300642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7368421055' to each side of the equation. -0.7368421055 + 0.7368421055 + x = 1.154300642 + 0.7368421055 Combine like terms: -0.7368421055 + 0.7368421055 = 0.0000000000 0.0000000000 + x = 1.154300642 + 0.7368421055 x = 1.154300642 + 0.7368421055 Combine like terms: 1.154300642 + 0.7368421055 = 1.8911427475 x = 1.8911427475 Simplifying x = 1.8911427475Subproblem 2
x + -0.7368421055 = -1.154300642 Simplifying x + -0.7368421055 = -1.154300642 Reorder the terms: -0.7368421055 + x = -1.154300642 Solving -0.7368421055 + x = -1.154300642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7368421055' to each side of the equation. -0.7368421055 + 0.7368421055 + x = -1.154300642 + 0.7368421055 Combine like terms: -0.7368421055 + 0.7368421055 = 0.0000000000 0.0000000000 + x = -1.154300642 + 0.7368421055 x = -1.154300642 + 0.7368421055 Combine like terms: -1.154300642 + 0.7368421055 = -0.4174585365 x = -0.4174585365 Simplifying x = -0.4174585365Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8911427475, -0.4174585365}Solution
x = {1.8911427475, -0.4174585365}
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