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Simplifying 4x2 + -4x = 0.035 Reorder the terms: -4x + 4x2 = 0.035 Solving -4x + 4x2 = 0.035 Solving for variable 'x'. Reorder the terms: -0.035 + -4x + 4x2 = 0.035 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 -0.035 + -4x + 4x2 = 0.000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.00875 + -1x + x2 = 0.000 Move the constant term to the right: Add '0.00875' to each side of the equation. -0.00875 + -1x + 0.00875 + x2 = 0.000 + 0.00875 Reorder the terms: -0.00875 + 0.00875 + -1x + x2 = 0.000 + 0.00875 Combine like terms: -0.00875 + 0.00875 = 0.00000 0.00000 + -1x + x2 = 0.000 + 0.00875 -1x + x2 = 0.000 + 0.00875 Combine like terms: 0.000 + 0.00875 = 0.00875 -1x + x2 = 0.00875 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 = 0.00875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.00875 + 0.25 Combine like terms: 0.00875 + 0.25 = 0.25875 0.25 + -1x + x2 = 0.25875 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.25875 Calculate the square root of the right side: 0.508674749 Break this problem into two subproblems by setting (x + -0.5) equal to 0.508674749 and -0.508674749.Subproblem 1
x + -0.5 = 0.508674749 Simplifying x + -0.5 = 0.508674749 Reorder the terms: -0.5 + x = 0.508674749 Solving -0.5 + x = 0.508674749 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 = 0.508674749 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.508674749 + 0.5 x = 0.508674749 + 0.5 Combine like terms: 0.508674749 + 0.5 = 1.008674749 x = 1.008674749 Simplifying x = 1.008674749Subproblem 2
x + -0.5 = -0.508674749 Simplifying x + -0.5 = -0.508674749 Reorder the terms: -0.5 + x = -0.508674749 Solving -0.5 + x = -0.508674749 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 = -0.508674749 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.508674749 + 0.5 x = -0.508674749 + 0.5 Combine like terms: -0.508674749 + 0.5 = -0.008674749 x = -0.008674749 Simplifying x = -0.008674749Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.008674749, -0.008674749}
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