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Simplifying 4x * 4x + 7x + -2 = 0 Reorder the terms for easier multiplication: 4 * 4x * x + 7x + -2 = 0 Multiply 4 * 4 16x * x + 7x + -2 = 0 Multiply x * x 16x2 + 7x + -2 = 0 Reorder the terms: -2 + 7x + 16x2 = 0 Solving -2 + 7x + 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'. -0.125 + 0.4375x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.4375x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.4375x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.4375x + x2 = 0 + 0.125 0.4375x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.4375x + x2 = 0.125 The x term is 0.4375x. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375x + 0.0478515625 + x2 = 0.125 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375x + x2 = 0.125 + 0.0478515625 Combine like terms: 0.125 + 0.0478515625 = 0.1728515625 0.0478515625 + 0.4375x + x2 = 0.1728515625 Factor a perfect square on the left side: (x + 0.21875)(x + 0.21875) = 0.1728515625 Calculate the square root of the right side: 0.415754209 Break this problem into two subproblems by setting (x + 0.21875) equal to 0.415754209 and -0.415754209.Subproblem 1
x + 0.21875 = 0.415754209 Simplifying x + 0.21875 = 0.415754209 Reorder the terms: 0.21875 + x = 0.415754209 Solving 0.21875 + x = 0.415754209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = 0.415754209 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = 0.415754209 + -0.21875 x = 0.415754209 + -0.21875 Combine like terms: 0.415754209 + -0.21875 = 0.197004209 x = 0.197004209 Simplifying x = 0.197004209Subproblem 2
x + 0.21875 = -0.415754209 Simplifying x + 0.21875 = -0.415754209 Reorder the terms: 0.21875 + x = -0.415754209 Solving 0.21875 + x = -0.415754209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + x = -0.415754209 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + x = -0.415754209 + -0.21875 x = -0.415754209 + -0.21875 Combine like terms: -0.415754209 + -0.21875 = -0.634504209 x = -0.634504209 Simplifying x = -0.634504209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.197004209, -0.634504209}
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