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Simplifying (-26x2) + -56x + 60 = 0 Reorder the terms: 60 + -56x + (-26x2) = 0 Solving 60 + -56x + (-26x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -28x + (-13x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -28x + (-13x2))' equal to zero and attempt to solve: Simplifying 30 + -28x + (-13x2) = 0 Solving 30 + -28x + (-13x2) = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -2.307692308 + 2.153846154x + x2 = 0 Move the constant term to the right: Add '2.307692308' to each side of the equation. -2.307692308 + 2.153846154x + 2.307692308 + x2 = 0 + 2.307692308 Reorder the terms: -2.307692308 + 2.307692308 + 2.153846154x + x2 = 0 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + 2.153846154x + x2 = 0 + 2.307692308 2.153846154x + x2 = 0 + 2.307692308 Combine like terms: 0 + 2.307692308 = 2.307692308 2.153846154x + x2 = 2.307692308 The x term is 2.153846154x. Take half its coefficient (1.076923077). Square it (1.159763314) and add it to both sides. Add '1.159763314' to each side of the equation. 2.153846154x + 1.159763314 + x2 = 2.307692308 + 1.159763314 Reorder the terms: 1.159763314 + 2.153846154x + x2 = 2.307692308 + 1.159763314 Combine like terms: 2.307692308 + 1.159763314 = 3.467455622 1.159763314 + 2.153846154x + x2 = 3.467455622 Factor a perfect square on the left side: ((x) + 1.076923077)((x) + 1.076923077) = 3.467455622 Calculate the square root of the right side: 1.862110529 Break this problem into two subproblems by setting ((x) + 1.076923077) equal to 1.862110529 and -1.862110529.Subproblem 1
(x) + 1.076923077 = 1.862110529 Simplifying (x) + 1.076923077 = 1.862110529 x + 1.076923077 = 1.862110529 Reorder the terms: 1.076923077 + x = 1.862110529 Solving 1.076923077 + x = 1.862110529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.076923077' to each side of the equation. 1.076923077 + -1.076923077 + x = 1.862110529 + -1.076923077 Combine like terms: 1.076923077 + -1.076923077 = 0.000000000 0.000000000 + x = 1.862110529 + -1.076923077 x = 1.862110529 + -1.076923077 Combine like terms: 1.862110529 + -1.076923077 = 0.785187452 x = 0.785187452 Simplifying x = 0.785187452Subproblem 2
(x) + 1.076923077 = -1.862110529 Simplifying (x) + 1.076923077 = -1.862110529 x + 1.076923077 = -1.862110529 Reorder the terms: 1.076923077 + x = -1.862110529 Solving 1.076923077 + x = -1.862110529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.076923077' to each side of the equation. 1.076923077 + -1.076923077 + x = -1.862110529 + -1.076923077 Combine like terms: 1.076923077 + -1.076923077 = 0.000000000 0.000000000 + x = -1.862110529 + -1.076923077 x = -1.862110529 + -1.076923077 Combine like terms: -1.862110529 + -1.076923077 = -2.939033606 x = -2.939033606 Simplifying x = -2.939033606Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.785187452, -2.939033606}Solution
x = {0.785187452, -2.939033606}
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