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Simplifying 13x2 + -8x + 5 = 48 Reorder the terms: 5 + -8x + 13x2 = 48 Solving 5 + -8x + 13x2 = 48 Solving for variable 'x'. Reorder the terms: 5 + -48 + -8x + 13x2 = 48 + -48 Combine like terms: 5 + -48 = -43 -43 + -8x + 13x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -43 + -8x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -3.307692308 + -0.6153846154x + x2 = 0 Move the constant term to the right: Add '3.307692308' to each side of the equation. -3.307692308 + -0.6153846154x + 3.307692308 + x2 = 0 + 3.307692308 Reorder the terms: -3.307692308 + 3.307692308 + -0.6153846154x + x2 = 0 + 3.307692308 Combine like terms: -3.307692308 + 3.307692308 = 0.000000000 0.000000000 + -0.6153846154x + x2 = 0 + 3.307692308 -0.6153846154x + x2 = 0 + 3.307692308 Combine like terms: 0 + 3.307692308 = 3.307692308 -0.6153846154x + x2 = 3.307692308 The x term is -0.6153846154x. Take half its coefficient (-0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. -0.6153846154x + 0.09467455622 + x2 = 3.307692308 + 0.09467455622 Reorder the terms: 0.09467455622 + -0.6153846154x + x2 = 3.307692308 + 0.09467455622 Combine like terms: 3.307692308 + 0.09467455622 = 3.40236686422 0.09467455622 + -0.6153846154x + x2 = 3.40236686422 Factor a perfect square on the left side: (x + -0.3076923077)(x + -0.3076923077) = 3.40236686422 Calculate the square root of the right side: 1.844550586 Break this problem into two subproblems by setting (x + -0.3076923077) equal to 1.844550586 and -1.844550586.Subproblem 1
x + -0.3076923077 = 1.844550586 Simplifying x + -0.3076923077 = 1.844550586 Reorder the terms: -0.3076923077 + x = 1.844550586 Solving -0.3076923077 + x = 1.844550586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + x = 1.844550586 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + x = 1.844550586 + 0.3076923077 x = 1.844550586 + 0.3076923077 Combine like terms: 1.844550586 + 0.3076923077 = 2.1522428937 x = 2.1522428937 Simplifying x = 2.1522428937Subproblem 2
x + -0.3076923077 = -1.844550586 Simplifying x + -0.3076923077 = -1.844550586 Reorder the terms: -0.3076923077 + x = -1.844550586 Solving -0.3076923077 + x = -1.844550586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + x = -1.844550586 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + x = -1.844550586 + 0.3076923077 x = -1.844550586 + 0.3076923077 Combine like terms: -1.844550586 + 0.3076923077 = -1.5368582783 x = -1.5368582783 Simplifying x = -1.5368582783Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1522428937, -1.5368582783}
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