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Simplifying x2 = (0.304)(0.760 + -1x) x2 = (0.760 * 0.304 + -1x * 0.304) x2 = (0.23104 + -0.304x) Solving x2 = 0.23104 + -0.304x Solving for variable 'x'. Reorder the terms: -0.23104 + 0.304x + x2 = 0.23104 + -0.304x + -0.23104 + 0.304x Reorder the terms: -0.23104 + 0.304x + x2 = 0.23104 + -0.23104 + -0.304x + 0.304x Combine like terms: 0.23104 + -0.23104 = 0.00000 -0.23104 + 0.304x + x2 = 0.00000 + -0.304x + 0.304x -0.23104 + 0.304x + x2 = -0.304x + 0.304x Combine like terms: -0.304x + 0.304x = 0.000 -0.23104 + 0.304x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.23104' to each side of the equation. -0.23104 + 0.304x + 0.23104 + x2 = 0.000 + 0.23104 Reorder the terms: -0.23104 + 0.23104 + 0.304x + x2 = 0.000 + 0.23104 Combine like terms: -0.23104 + 0.23104 = 0.00000 0.00000 + 0.304x + x2 = 0.000 + 0.23104 0.304x + x2 = 0.000 + 0.23104 Combine like terms: 0.000 + 0.23104 = 0.23104 0.304x + x2 = 0.23104 The x term is 0.304x. Take half its coefficient (0.152). Square it (0.023104) and add it to both sides. Add '0.023104' to each side of the equation. 0.304x + 0.023104 + x2 = 0.23104 + 0.023104 Reorder the terms: 0.023104 + 0.304x + x2 = 0.23104 + 0.023104 Combine like terms: 0.23104 + 0.023104 = 0.254144 0.023104 + 0.304x + x2 = 0.254144 Factor a perfect square on the left side: (x + 0.152)(x + 0.152) = 0.254144 Calculate the square root of the right side: 0.504126968 Break this problem into two subproblems by setting (x + 0.152) equal to 0.504126968 and -0.504126968.Subproblem 1
x + 0.152 = 0.504126968 Simplifying x + 0.152 = 0.504126968 Reorder the terms: 0.152 + x = 0.504126968 Solving 0.152 + x = 0.504126968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.152' to each side of the equation. 0.152 + -0.152 + x = 0.504126968 + -0.152 Combine like terms: 0.152 + -0.152 = 0.000 0.000 + x = 0.504126968 + -0.152 x = 0.504126968 + -0.152 Combine like terms: 0.504126968 + -0.152 = 0.352126968 x = 0.352126968 Simplifying x = 0.352126968Subproblem 2
x + 0.152 = -0.504126968 Simplifying x + 0.152 = -0.504126968 Reorder the terms: 0.152 + x = -0.504126968 Solving 0.152 + x = -0.504126968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.152' to each side of the equation. 0.152 + -0.152 + x = -0.504126968 + -0.152 Combine like terms: 0.152 + -0.152 = 0.000 0.000 + x = -0.504126968 + -0.152 x = -0.504126968 + -0.152 Combine like terms: -0.504126968 + -0.152 = -0.656126968 x = -0.656126968 Simplifying x = -0.656126968Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.352126968, -0.656126968}
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