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Simplifying 2x(4x + -3) = 10x + -1 Reorder the terms: 2x(-3 + 4x) = 10x + -1 (-3 * 2x + 4x * 2x) = 10x + -1 (-6x + 8x2) = 10x + -1 Reorder the terms: -6x + 8x2 = -1 + 10x Solving -6x + 8x2 = -1 + 10x Solving for variable 'x'. Reorder the terms: 1 + -6x + -10x + 8x2 = -1 + 10x + 1 + -10x Combine like terms: -6x + -10x = -16x 1 + -16x + 8x2 = -1 + 10x + 1 + -10x Reorder the terms: 1 + -16x + 8x2 = -1 + 1 + 10x + -10x Combine like terms: -1 + 1 = 0 1 + -16x + 8x2 = 0 + 10x + -10x 1 + -16x + 8x2 = 10x + -10x Combine like terms: 10x + -10x = 0 1 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -2x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -2x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -2x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -2x + x2 = 0 + -0.125 -2x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -2x + x2 = -0.125 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.125 + 1 Reorder the terms: 1 + -2x + x2 = -0.125 + 1 Combine like terms: -0.125 + 1 = 0.875 1 + -2x + x2 = 0.875 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (x + -1) equal to 0.935414347 and -0.935414347.Subproblem 1
x + -1 = 0.935414347 Simplifying x + -1 = 0.935414347 Reorder the terms: -1 + x = 0.935414347 Solving -1 + x = 0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.935414347 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.935414347 + 1 x = 0.935414347 + 1 Combine like terms: 0.935414347 + 1 = 1.935414347 x = 1.935414347 Simplifying x = 1.935414347Subproblem 2
x + -1 = -0.935414347 Simplifying x + -1 = -0.935414347 Reorder the terms: -1 + x = -0.935414347 Solving -1 + x = -0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.935414347 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.935414347 + 1 x = -0.935414347 + 1 Combine like terms: -0.935414347 + 1 = 0.064585653 x = 0.064585653 Simplifying x = 0.064585653Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.935414347, 0.064585653}
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