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Simplifying 15x2 + 46x + -35 = 0 Reorder the terms: -35 + 46x + 15x2 = 0 Solving -35 + 46x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.333333333 + 3.066666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 3.066666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 3.066666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 3.066666667x + x2 = 0 + 2.333333333 3.066666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 3.066666667x + x2 = 2.333333333 The x term is 3.066666667x. Take half its coefficient (1.533333334). Square it (2.351111113) and add it to both sides. Add '2.351111113' to each side of the equation. 3.066666667x + 2.351111113 + x2 = 2.333333333 + 2.351111113 Reorder the terms: 2.351111113 + 3.066666667x + x2 = 2.333333333 + 2.351111113 Combine like terms: 2.333333333 + 2.351111113 = 4.684444446 2.351111113 + 3.066666667x + x2 = 4.684444446 Factor a perfect square on the left side: (x + 1.533333334)(x + 1.533333334) = 4.684444446 Calculate the square root of the right side: 2.164357744 Break this problem into two subproblems by setting (x + 1.533333334) equal to 2.164357744 and -2.164357744.Subproblem 1
x + 1.533333334 = 2.164357744 Simplifying x + 1.533333334 = 2.164357744 Reorder the terms: 1.533333334 + x = 2.164357744 Solving 1.533333334 + x = 2.164357744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.533333334' to each side of the equation. 1.533333334 + -1.533333334 + x = 2.164357744 + -1.533333334 Combine like terms: 1.533333334 + -1.533333334 = 0.000000000 0.000000000 + x = 2.164357744 + -1.533333334 x = 2.164357744 + -1.533333334 Combine like terms: 2.164357744 + -1.533333334 = 0.63102441 x = 0.63102441 Simplifying x = 0.63102441Subproblem 2
x + 1.533333334 = -2.164357744 Simplifying x + 1.533333334 = -2.164357744 Reorder the terms: 1.533333334 + x = -2.164357744 Solving 1.533333334 + x = -2.164357744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.533333334' to each side of the equation. 1.533333334 + -1.533333334 + x = -2.164357744 + -1.533333334 Combine like terms: 1.533333334 + -1.533333334 = 0.000000000 0.000000000 + x = -2.164357744 + -1.533333334 x = -2.164357744 + -1.533333334 Combine like terms: -2.164357744 + -1.533333334 = -3.697691078 x = -3.697691078 Simplifying x = -3.697691078Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.63102441, -3.697691078}
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