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Simplifying 6x2 + 4x + -15 = 0 Reorder the terms: -15 + 4x + 6x2 = 0 Solving -15 + 4x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.6666666667x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.6666666667x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 2.5 0.6666666667x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.6666666667x + x2 = 2.5 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 2.5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 2.5 + 0.1111111112 Combine like terms: 2.5 + 0.1111111112 = 2.6111111112 0.1111111112 + 0.6666666667x + x2 = 2.6111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 2.6111111112 Calculate the square root of the right side: 1.615893286 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.615893286 and -1.615893286.Subproblem 1
x + 0.3333333334 = 1.615893286 Simplifying x + 0.3333333334 = 1.615893286 Reorder the terms: 0.3333333334 + x = 1.615893286 Solving 0.3333333334 + x = 1.615893286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.615893286 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.615893286 + -0.3333333334 x = 1.615893286 + -0.3333333334 Combine like terms: 1.615893286 + -0.3333333334 = 1.2825599526 x = 1.2825599526 Simplifying x = 1.2825599526Subproblem 2
x + 0.3333333334 = -1.615893286 Simplifying x + 0.3333333334 = -1.615893286 Reorder the terms: 0.3333333334 + x = -1.615893286 Solving 0.3333333334 + x = -1.615893286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.615893286 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.615893286 + -0.3333333334 x = -1.615893286 + -0.3333333334 Combine like terms: -1.615893286 + -0.3333333334 = -1.9492266194 x = -1.9492266194 Simplifying x = -1.9492266194Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2825599526, -1.9492266194}
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