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Simplifying 4x(2x + -1) = 7 Reorder the terms: 4x(-1 + 2x) = 7 (-1 * 4x + 2x * 4x) = 7 (-4x + 8x2) = 7 Solving -4x + 8x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -4x + 8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.5x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.5x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.5x + x2 = 0 + 0.875 -0.5x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.5x + x2 = 0.875 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.875 + 0.0625 Combine like terms: 0.875 + 0.0625 = 0.9375 0.0625 + -0.5x + x2 = 0.9375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (x + -0.25) equal to 0.968245837 and -0.968245837.Subproblem 1
x + -0.25 = 0.968245837 Simplifying x + -0.25 = 0.968245837 Reorder the terms: -0.25 + x = 0.968245837 Solving -0.25 + x = 0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.968245837 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.968245837 + 0.25 x = 0.968245837 + 0.25 Combine like terms: 0.968245837 + 0.25 = 1.218245837 x = 1.218245837 Simplifying x = 1.218245837Subproblem 2
x + -0.25 = -0.968245837 Simplifying x + -0.25 = -0.968245837 Reorder the terms: -0.25 + x = -0.968245837 Solving -0.25 + x = -0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.968245837 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.968245837 + 0.25 x = -0.968245837 + 0.25 Combine like terms: -0.968245837 + 0.25 = -0.718245837 x = -0.718245837 Simplifying x = -0.718245837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.218245837, -0.718245837}
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