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Simplifying -1(3x + -2)(5x + 3) + -1x2 = 0 Reorder the terms: -1(-2 + 3x)(5x + 3) + -1x2 = 0 Reorder the terms: -1(-2 + 3x)(3 + 5x) + -1x2 = 0 Multiply (-2 + 3x) * (3 + 5x) -1(-2(3 + 5x) + 3x * (3 + 5x)) + -1x2 = 0 -1((3 * -2 + 5x * -2) + 3x * (3 + 5x)) + -1x2 = 0 -1((-6 + -10x) + 3x * (3 + 5x)) + -1x2 = 0 -1(-6 + -10x + (3 * 3x + 5x * 3x)) + -1x2 = 0 -1(-6 + -10x + (9x + 15x2)) + -1x2 = 0 Combine like terms: -10x + 9x = -1x -1(-6 + -1x + 15x2) + -1x2 = 0 (-6 * -1 + -1x * -1 + 15x2 * -1) + -1x2 = 0 (6 + 1x + -15x2) + -1x2 = 0 Combine like terms: -15x2 + -1x2 = -16x2 6 + 1x + -16x2 = 0 Solving 6 + 1x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.375 + -0.0625x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.0625x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.0625x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.0625x + x2 = 0 + 0.375 -0.0625x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.0625x + x2 = 0.375 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 0.375 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 0.375 + 0.0009765625 Combine like terms: 0.375 + 0.0009765625 = 0.3759765625 0.0009765625 + -0.0625x + x2 = 0.3759765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 0.3759765625 Calculate the square root of the right side: 0.613169277 Break this problem into two subproblems by setting (x + -0.03125) equal to 0.613169277 and -0.613169277.Subproblem 1
x + -0.03125 = 0.613169277 Simplifying x + -0.03125 = 0.613169277 Reorder the terms: -0.03125 + x = 0.613169277 Solving -0.03125 + x = 0.613169277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 0.613169277 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 0.613169277 + 0.03125 x = 0.613169277 + 0.03125 Combine like terms: 0.613169277 + 0.03125 = 0.644419277 x = 0.644419277 Simplifying x = 0.644419277Subproblem 2
x + -0.03125 = -0.613169277 Simplifying x + -0.03125 = -0.613169277 Reorder the terms: -0.03125 + x = -0.613169277 Solving -0.03125 + x = -0.613169277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -0.613169277 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -0.613169277 + 0.03125 x = -0.613169277 + 0.03125 Combine like terms: -0.613169277 + 0.03125 = -0.581919277 x = -0.581919277 Simplifying x = -0.581919277Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.644419277, -0.581919277}
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