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Simplifying 13x2 + -39x + 28 = 0 Reorder the terms: 28 + -39x + 13x2 = 0 Solving 28 + -39x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 2.153846154 + -3x + x2 = 0 Move the constant term to the right: Add '-2.153846154' to each side of the equation. 2.153846154 + -3x + -2.153846154 + x2 = 0 + -2.153846154 Reorder the terms: 2.153846154 + -2.153846154 + -3x + x2 = 0 + -2.153846154 Combine like terms: 2.153846154 + -2.153846154 = 0.000000000 0.000000000 + -3x + x2 = 0 + -2.153846154 -3x + x2 = 0 + -2.153846154 Combine like terms: 0 + -2.153846154 = -2.153846154 -3x + x2 = -2.153846154 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.153846154 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.153846154 + 2.25 Combine like terms: -2.153846154 + 2.25 = 0.096153846 2.25 + -3x + x2 = 0.096153846 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.096153846 Calculate the square root of the right side: 0.310086836 Break this problem into two subproblems by setting (x + -1.5) equal to 0.310086836 and -0.310086836.Subproblem 1
x + -1.5 = 0.310086836 Simplifying x + -1.5 = 0.310086836 Reorder the terms: -1.5 + x = 0.310086836 Solving -1.5 + x = 0.310086836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.310086836 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.310086836 + 1.5 x = 0.310086836 + 1.5 Combine like terms: 0.310086836 + 1.5 = 1.810086836 x = 1.810086836 Simplifying x = 1.810086836Subproblem 2
x + -1.5 = -0.310086836 Simplifying x + -1.5 = -0.310086836 Reorder the terms: -1.5 + x = -0.310086836 Solving -1.5 + x = -0.310086836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.310086836 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.310086836 + 1.5 x = -0.310086836 + 1.5 Combine like terms: -0.310086836 + 1.5 = 1.189913164 x = 1.189913164 Simplifying x = 1.189913164Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.810086836, 1.189913164}
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