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Simplifying 4 = (0.300 + x)(0.200 + x) Multiply (0.300 + x) * (0.200 + x) 4 = (0.300(0.200 + x) + x(0.200 + x)) 4 = ((0.200 * 0.300 + x * 0.300) + x(0.200 + x)) 4 = ((0.06 + 0.300x) + x(0.200 + x)) 4 = (0.06 + 0.300x + (0.200 * x + x * x)) 4 = (0.06 + 0.300x + (0.200x + x2)) Combine like terms: 0.300x + 0.200x = 0.5x 4 = (0.06 + 0.5x + x2) Solving 4 = 0.06 + 0.5x + x2 Solving for variable 'x'. Combine like terms: 4 + -0.06 = 3.94 3.94 + -0.5x + -1x2 = 0.06 + 0.5x + x2 + -0.06 + -0.5x + -1x2 Reorder the terms: 3.94 + -0.5x + -1x2 = 0.06 + -0.06 + 0.5x + -0.5x + x2 + -1x2 Combine like terms: 0.06 + -0.06 = 0.00 3.94 + -0.5x + -1x2 = 0.00 + 0.5x + -0.5x + x2 + -1x2 3.94 + -0.5x + -1x2 = 0.5x + -0.5x + x2 + -1x2 Combine like terms: 0.5x + -0.5x = 0.0 3.94 + -0.5x + -1x2 = 0.0 + x2 + -1x2 3.94 + -0.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3.94 + -0.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3.94 + 0.5x + x2 = 0 Move the constant term to the right: Add '3.94' to each side of the equation. -3.94 + 0.5x + 3.94 + x2 = 0 + 3.94 Reorder the terms: -3.94 + 3.94 + 0.5x + x2 = 0 + 3.94 Combine like terms: -3.94 + 3.94 = 0.00 0.00 + 0.5x + x2 = 0 + 3.94 0.5x + x2 = 0 + 3.94 Combine like terms: 0 + 3.94 = 3.94 0.5x + x2 = 3.94 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 3.94 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 3.94 + 0.0625 Combine like terms: 3.94 + 0.0625 = 4.0025 0.0625 + 0.5x + x2 = 4.0025 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.0025 Calculate the square root of the right side: 2.000624902 Break this problem into two subproblems by setting (x + 0.25) equal to 2.000624902 and -2.000624902.Subproblem 1
x + 0.25 = 2.000624902 Simplifying x + 0.25 = 2.000624902 Reorder the terms: 0.25 + x = 2.000624902 Solving 0.25 + x = 2.000624902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.000624902 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.000624902 + -0.25 x = 2.000624902 + -0.25 Combine like terms: 2.000624902 + -0.25 = 1.750624902 x = 1.750624902 Simplifying x = 1.750624902Subproblem 2
x + 0.25 = -2.000624902 Simplifying x + 0.25 = -2.000624902 Reorder the terms: 0.25 + x = -2.000624902 Solving 0.25 + x = -2.000624902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.000624902 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.000624902 + -0.25 x = -2.000624902 + -0.25 Combine like terms: -2.000624902 + -0.25 = -2.250624902 x = -2.250624902 Simplifying x = -2.250624902Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.750624902, -2.250624902}
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