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Simplifying (x2 + -1x) + -14(x2 + -1x) + 24 = 0 Reorder the terms: (-1x + x2) + -14(x2 + -1x) + 24 = 0 Remove parenthesis around (-1x + x2) -1x + x2 + -14(x2 + -1x) + 24 = 0 Reorder the terms: -1x + x2 + -14(-1x + x2) + 24 = 0 -1x + x2 + (-1x * -14 + x2 * -14) + 24 = 0 -1x + x2 + (14x + -14x2) + 24 = 0 Reorder the terms: 24 + -1x + 14x + x2 + -14x2 = 0 Combine like terms: -1x + 14x = 13x 24 + 13x + x2 + -14x2 = 0 Combine like terms: x2 + -14x2 = -13x2 24 + 13x + -13x2 = 0 Solving 24 + 13x + -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'. -1.846153846 + -1x + x2 = 0 Move the constant term to the right: Add '1.846153846' to each side of the equation. -1.846153846 + -1x + 1.846153846 + x2 = 0 + 1.846153846 Reorder the terms: -1.846153846 + 1.846153846 + -1x + x2 = 0 + 1.846153846 Combine like terms: -1.846153846 + 1.846153846 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.846153846 -1x + x2 = 0 + 1.846153846 Combine like terms: 0 + 1.846153846 = 1.846153846 -1x + x2 = 1.846153846 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.846153846 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.846153846 + 0.25 Combine like terms: 1.846153846 + 0.25 = 2.096153846 0.25 + -1x + x2 = 2.096153846 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.096153846 Calculate the square root of the right side: 1.447810017 Break this problem into two subproblems by setting (x + -0.5) equal to 1.447810017 and -1.447810017.Subproblem 1
x + -0.5 = 1.447810017 Simplifying x + -0.5 = 1.447810017 Reorder the terms: -0.5 + x = 1.447810017 Solving -0.5 + x = 1.447810017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.447810017 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.447810017 + 0.5 x = 1.447810017 + 0.5 Combine like terms: 1.447810017 + 0.5 = 1.947810017 x = 1.947810017 Simplifying x = 1.947810017Subproblem 2
x + -0.5 = -1.447810017 Simplifying x + -0.5 = -1.447810017 Reorder the terms: -0.5 + x = -1.447810017 Solving -0.5 + x = -1.447810017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.447810017 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.447810017 + 0.5 x = -1.447810017 + 0.5 Combine like terms: -1.447810017 + 0.5 = -0.947810017 x = -0.947810017 Simplifying x = -0.947810017Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.947810017, -0.947810017}
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