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Simplifying 13x2 + 53 = 56x Reorder the terms: 53 + 13x2 = 56x Solving 53 + 13x2 = 56x Solving for variable 'x'. Reorder the terms: 53 + -56x + 13x2 = 56x + -56x Combine like terms: 56x + -56x = 0 53 + -56x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 4.076923077 + -4.307692308x + x2 = 0 Move the constant term to the right: Add '-4.076923077' to each side of the equation. 4.076923077 + -4.307692308x + -4.076923077 + x2 = 0 + -4.076923077 Reorder the terms: 4.076923077 + -4.076923077 + -4.307692308x + x2 = 0 + -4.076923077 Combine like terms: 4.076923077 + -4.076923077 = 0.000000000 0.000000000 + -4.307692308x + x2 = 0 + -4.076923077 -4.307692308x + x2 = 0 + -4.076923077 Combine like terms: 0 + -4.076923077 = -4.076923077 -4.307692308x + x2 = -4.076923077 The x term is -4.307692308x. Take half its coefficient (-2.153846154). Square it (4.639053255) and add it to both sides. Add '4.639053255' to each side of the equation. -4.307692308x + 4.639053255 + x2 = -4.076923077 + 4.639053255 Reorder the terms: 4.639053255 + -4.307692308x + x2 = -4.076923077 + 4.639053255 Combine like terms: -4.076923077 + 4.639053255 = 0.562130178 4.639053255 + -4.307692308x + x2 = 0.562130178 Factor a perfect square on the left side: (x + -2.153846154)(x + -2.153846154) = 0.562130178 Calculate the square root of the right side: 0.749753411 Break this problem into two subproblems by setting (x + -2.153846154) equal to 0.749753411 and -0.749753411.Subproblem 1
x + -2.153846154 = 0.749753411 Simplifying x + -2.153846154 = 0.749753411 Reorder the terms: -2.153846154 + x = 0.749753411 Solving -2.153846154 + x = 0.749753411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.153846154' to each side of the equation. -2.153846154 + 2.153846154 + x = 0.749753411 + 2.153846154 Combine like terms: -2.153846154 + 2.153846154 = 0.000000000 0.000000000 + x = 0.749753411 + 2.153846154 x = 0.749753411 + 2.153846154 Combine like terms: 0.749753411 + 2.153846154 = 2.903599565 x = 2.903599565 Simplifying x = 2.903599565Subproblem 2
x + -2.153846154 = -0.749753411 Simplifying x + -2.153846154 = -0.749753411 Reorder the terms: -2.153846154 + x = -0.749753411 Solving -2.153846154 + x = -0.749753411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.153846154' to each side of the equation. -2.153846154 + 2.153846154 + x = -0.749753411 + 2.153846154 Combine like terms: -2.153846154 + 2.153846154 = 0.000000000 0.000000000 + x = -0.749753411 + 2.153846154 x = -0.749753411 + 2.153846154 Combine like terms: -0.749753411 + 2.153846154 = 1.404092743 x = 1.404092743 Simplifying x = 1.404092743Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.903599565, 1.404092743}
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