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Simplifying 26x2 + -30x + -26 = 0 Reorder the terms: -26 + -30x + 26x2 = 0 Solving -26 + -30x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -15x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -15x + 13x2)' equal to zero and attempt to solve: Simplifying -13 + -15x + 13x2 = 0 Solving -13 + -15x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1 + -1.153846154x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.153846154x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.153846154x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.153846154x + x2 = 0 + 1 -1.153846154x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.153846154x + x2 = 1 The x term is -1.153846154x. Take half its coefficient (-0.576923077). Square it (0.3328402368) and add it to both sides. Add '0.3328402368' to each side of the equation. -1.153846154x + 0.3328402368 + x2 = 1 + 0.3328402368 Reorder the terms: 0.3328402368 + -1.153846154x + x2 = 1 + 0.3328402368 Combine like terms: 1 + 0.3328402368 = 1.3328402368 0.3328402368 + -1.153846154x + x2 = 1.3328402368 Factor a perfect square on the left side: (x + -0.576923077)(x + -0.576923077) = 1.3328402368 Calculate the square root of the right side: 1.154487002 Break this problem into two subproblems by setting (x + -0.576923077) equal to 1.154487002 and -1.154487002.Subproblem 1
x + -0.576923077 = 1.154487002 Simplifying x + -0.576923077 = 1.154487002 Reorder the terms: -0.576923077 + x = 1.154487002 Solving -0.576923077 + x = 1.154487002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.576923077' to each side of the equation. -0.576923077 + 0.576923077 + x = 1.154487002 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = 1.154487002 + 0.576923077 x = 1.154487002 + 0.576923077 Combine like terms: 1.154487002 + 0.576923077 = 1.731410079 x = 1.731410079 Simplifying x = 1.731410079Subproblem 2
x + -0.576923077 = -1.154487002 Simplifying x + -0.576923077 = -1.154487002 Reorder the terms: -0.576923077 + x = -1.154487002 Solving -0.576923077 + x = -1.154487002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.576923077' to each side of the equation. -0.576923077 + 0.576923077 + x = -1.154487002 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = -1.154487002 + 0.576923077 x = -1.154487002 + 0.576923077 Combine like terms: -1.154487002 + 0.576923077 = -0.577563925 x = -0.577563925 Simplifying x = -0.577563925Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.731410079, -0.577563925}Solution
x = {1.731410079, -0.577563925}
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