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Simplifying 4x(1 + -1x) = 0.88 (1 * 4x + -1x * 4x) = 0.88 (4x + -4x2) = 0.88 Solving 4x + -4x2 = 0.88 Solving for variable 'x'. Reorder the terms: -0.88 + 4x + -4x2 = 0.88 + -0.88 Combine like terms: 0.88 + -0.88 = 0.00 -0.88 + 4x + -4x2 = 0.00 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.22 + -1x + x2 = 0.00 Move the constant term to the right: Add '-0.22' to each side of the equation. 0.22 + -1x + -0.22 + x2 = 0.00 + -0.22 Reorder the terms: 0.22 + -0.22 + -1x + x2 = 0.00 + -0.22 Combine like terms: 0.22 + -0.22 = 0.00 0.00 + -1x + x2 = 0.00 + -0.22 -1x + x2 = 0.00 + -0.22 Combine like terms: 0.00 + -0.22 = -0.22 -1x + x2 = -0.22 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.22 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.22 + 0.25 Combine like terms: -0.22 + 0.25 = 0.03 0.25 + -1x + x2 = 0.03 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.03 Calculate the square root of the right side: 0.173205081 Break this problem into two subproblems by setting (x + -0.5) equal to 0.173205081 and -0.173205081.Subproblem 1
x + -0.5 = 0.173205081 Simplifying x + -0.5 = 0.173205081 Reorder the terms: -0.5 + x = 0.173205081 Solving -0.5 + x = 0.173205081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.173205081 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.173205081 + 0.5 x = 0.173205081 + 0.5 Combine like terms: 0.173205081 + 0.5 = 0.673205081 x = 0.673205081 Simplifying x = 0.673205081Subproblem 2
x + -0.5 = -0.173205081 Simplifying x + -0.5 = -0.173205081 Reorder the terms: -0.5 + x = -0.173205081 Solving -0.5 + x = -0.173205081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.173205081 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.173205081 + 0.5 x = -0.173205081 + 0.5 Combine like terms: -0.173205081 + 0.5 = 0.326794919 x = 0.326794919 Simplifying x = 0.326794919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.673205081, 0.326794919}
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