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Simplifying 11x2 + -2x + 13 = 17x2 + -15x + 3 Reorder the terms: 13 + -2x + 11x2 = 17x2 + -15x + 3 Reorder the terms: 13 + -2x + 11x2 = 3 + -15x + 17x2 Solving 13 + -2x + 11x2 = 3 + -15x + 17x2 Solving for variable 'x'. Reorder the terms: 13 + -3 + -2x + 15x + 11x2 + -17x2 = 3 + -15x + 17x2 + -3 + 15x + -17x2 Combine like terms: 13 + -3 = 10 10 + -2x + 15x + 11x2 + -17x2 = 3 + -15x + 17x2 + -3 + 15x + -17x2 Combine like terms: -2x + 15x = 13x 10 + 13x + 11x2 + -17x2 = 3 + -15x + 17x2 + -3 + 15x + -17x2 Combine like terms: 11x2 + -17x2 = -6x2 10 + 13x + -6x2 = 3 + -15x + 17x2 + -3 + 15x + -17x2 Reorder the terms: 10 + 13x + -6x2 = 3 + -3 + -15x + 15x + 17x2 + -17x2 Combine like terms: 3 + -3 = 0 10 + 13x + -6x2 = 0 + -15x + 15x + 17x2 + -17x2 10 + 13x + -6x2 = -15x + 15x + 17x2 + -17x2 Combine like terms: -15x + 15x = 0 10 + 13x + -6x2 = 0 + 17x2 + -17x2 10 + 13x + -6x2 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 10 + 13x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.666666667 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -2.166666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -2.166666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -2.166666667x + x2 = 0 + 1.666666667 -2.166666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -2.166666667x + x2 = 1.666666667 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 1.666666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 1.666666667 + 1.173611113 Combine like terms: 1.666666667 + 1.173611113 = 2.84027778 1.173611113 + -2.166666667x + x2 = 2.84027778 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 2.84027778 Calculate the square root of the right side: 1.685312369 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.685312369 and -1.685312369.Subproblem 1
x + -1.083333334 = 1.685312369 Simplifying x + -1.083333334 = 1.685312369 Reorder the terms: -1.083333334 + x = 1.685312369 Solving -1.083333334 + x = 1.685312369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.685312369 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.685312369 + 1.083333334 x = 1.685312369 + 1.083333334 Combine like terms: 1.685312369 + 1.083333334 = 2.768645703 x = 2.768645703 Simplifying x = 2.768645703Subproblem 2
x + -1.083333334 = -1.685312369 Simplifying x + -1.083333334 = -1.685312369 Reorder the terms: -1.083333334 + x = -1.685312369 Solving -1.083333334 + x = -1.685312369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.685312369 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.685312369 + 1.083333334 x = -1.685312369 + 1.083333334 Combine like terms: -1.685312369 + 1.083333334 = -0.601979035 x = -0.601979035 Simplifying x = -0.601979035Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.768645703, -0.601979035}
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