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Simplifying x = (5x + -4)(5x + 4) Reorder the terms: x = (-4 + 5x)(5x + 4) Reorder the terms: x = (-4 + 5x)(4 + 5x) Multiply (-4 + 5x) * (4 + 5x) x = (-4(4 + 5x) + 5x * (4 + 5x)) x = ((4 * -4 + 5x * -4) + 5x * (4 + 5x)) x = ((-16 + -20x) + 5x * (4 + 5x)) x = (-16 + -20x + (4 * 5x + 5x * 5x)) x = (-16 + -20x + (20x + 25x2)) Combine like terms: -20x + 20x = 0 x = (-16 + 0 + 25x2) x = (-16 + 25x2) Solving x = -16 + 25x2 Solving for variable 'x'. Reorder the terms: 16 + x + -25x2 = -16 + 25x2 + 16 + -25x2 Reorder the terms: 16 + x + -25x2 = -16 + 16 + 25x2 + -25x2 Combine like terms: -16 + 16 = 0 16 + x + -25x2 = 0 + 25x2 + -25x2 16 + x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 16 + x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.64 + -0.04x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -0.04x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -0.04x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -0.04x + x2 = 0 + 0.64 -0.04x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -0.04x + x2 = 0.64 The x term is x. 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. -0.04x + 0.25 + x2 = 0.64 + 0.25 Reorder the terms: 0.25 + -0.04x + x2 = 0.64 + 0.25 Combine like terms: 0.64 + 0.25 = 0.89 0.25 + -0.04x + x2 = 0.89 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + 0.5) equal to 0.943398113 and -0.943398113.Subproblem 1
x + 0.5 = 0.943398113 Simplifying x + 0.5 = 0.943398113 Reorder the terms: 0.5 + x = 0.943398113 Solving 0.5 + x = 0.943398113 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 = 0.943398113 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.943398113 + -0.5 x = 0.943398113 + -0.5 Combine like terms: 0.943398113 + -0.5 = 0.443398113 x = 0.443398113 Simplifying x = 0.443398113Subproblem 2
x + 0.5 = -0.943398113 Simplifying x + 0.5 = -0.943398113 Reorder the terms: 0.5 + x = -0.943398113 Solving 0.5 + x = -0.943398113 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 = -0.943398113 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.943398113 + -0.5 x = -0.943398113 + -0.5 Combine like terms: -0.943398113 + -0.5 = -1.443398113 x = -1.443398113 Simplifying x = -1.443398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.443398113, -1.443398113}
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