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Simplifying 0.64x2 + -0.128x + -4 = 0 Reorder the terms: -4 + -0.128x + 0.64x2 = 0 Solving -4 + -0.128x + 0.64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -6.25 + -0.2x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -0.2x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -0.2x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -0.2x + x2 = 0 + 6.25 -0.2x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -0.2x + x2 = 6.25 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 6.25 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 6.25 + 0.01 Combine like terms: 6.25 + 0.01 = 6.26 0.01 + -0.2x + x2 = 6.26 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 6.26 Calculate the square root of the right side: 2.501999201 Break this problem into two subproblems by setting (x + -0.1) equal to 2.501999201 and -2.501999201.Subproblem 1
x + -0.1 = 2.501999201 Simplifying x + -0.1 = 2.501999201 Reorder the terms: -0.1 + x = 2.501999201 Solving -0.1 + x = 2.501999201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 2.501999201 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 2.501999201 + 0.1 x = 2.501999201 + 0.1 Combine like terms: 2.501999201 + 0.1 = 2.601999201 x = 2.601999201 Simplifying x = 2.601999201Subproblem 2
x + -0.1 = -2.501999201 Simplifying x + -0.1 = -2.501999201 Reorder the terms: -0.1 + x = -2.501999201 Solving -0.1 + x = -2.501999201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -2.501999201 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -2.501999201 + 0.1 x = -2.501999201 + 0.1 Combine like terms: -2.501999201 + 0.1 = -2.401999201 x = -2.401999201 Simplifying x = -2.401999201Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.601999201, -2.401999201}
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