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Simplifying 7 = (0.2 + -1x)(0.34 + -1x) Multiply (0.2 + -1x) * (0.34 + -1x) 7 = (0.2(0.34 + -1x) + -1x * (0.34 + -1x)) 7 = ((0.34 * 0.2 + -1x * 0.2) + -1x * (0.34 + -1x)) 7 = ((0.068 + -0.2x) + -1x * (0.34 + -1x)) 7 = (0.068 + -0.2x + (0.34 * -1x + -1x * -1x)) 7 = (0.068 + -0.2x + (-0.34x + 1x2)) Combine like terms: -0.2x + -0.34x = -0.54x 7 = (0.068 + -0.54x + 1x2) Solving 7 = 0.068 + -0.54x + 1x2 Solving for variable 'x'. Combine like terms: 7 + -0.068 = 6.932 6.932 + 0.54x + -1x2 = 0.068 + -0.54x + 1x2 + -0.068 + 0.54x + -1x2 Reorder the terms: 6.932 + 0.54x + -1x2 = 0.068 + -0.068 + -0.54x + 0.54x + 1x2 + -1x2 Combine like terms: 0.068 + -0.068 = 0.000 6.932 + 0.54x + -1x2 = 0.000 + -0.54x + 0.54x + 1x2 + -1x2 6.932 + 0.54x + -1x2 = -0.54x + 0.54x + 1x2 + -1x2 Combine like terms: -0.54x + 0.54x = 0.00 6.932 + 0.54x + -1x2 = 0.00 + 1x2 + -1x2 6.932 + 0.54x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 6.932 + 0.54x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6.932 + -0.54x + x2 = 0 Move the constant term to the right: Add '6.932' to each side of the equation. -6.932 + -0.54x + 6.932 + x2 = 0 + 6.932 Reorder the terms: -6.932 + 6.932 + -0.54x + x2 = 0 + 6.932 Combine like terms: -6.932 + 6.932 = 0.000 0.000 + -0.54x + x2 = 0 + 6.932 -0.54x + x2 = 0 + 6.932 Combine like terms: 0 + 6.932 = 6.932 -0.54x + x2 = 6.932 The x term is -0.54x. Take half its coefficient (-0.27). Square it (0.0729) and add it to both sides. Add '0.0729' to each side of the equation. -0.54x + 0.0729 + x2 = 6.932 + 0.0729 Reorder the terms: 0.0729 + -0.54x + x2 = 6.932 + 0.0729 Combine like terms: 6.932 + 0.0729 = 7.0049 0.0729 + -0.54x + x2 = 7.0049 Factor a perfect square on the left side: (x + -0.27)(x + -0.27) = 7.0049 Calculate the square root of the right side: 2.646677162 Break this problem into two subproblems by setting (x + -0.27) equal to 2.646677162 and -2.646677162.Subproblem 1
x + -0.27 = 2.646677162 Simplifying x + -0.27 = 2.646677162 Reorder the terms: -0.27 + x = 2.646677162 Solving -0.27 + x = 2.646677162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.27' to each side of the equation. -0.27 + 0.27 + x = 2.646677162 + 0.27 Combine like terms: -0.27 + 0.27 = 0.00 0.00 + x = 2.646677162 + 0.27 x = 2.646677162 + 0.27 Combine like terms: 2.646677162 + 0.27 = 2.916677162 x = 2.916677162 Simplifying x = 2.916677162Subproblem 2
x + -0.27 = -2.646677162 Simplifying x + -0.27 = -2.646677162 Reorder the terms: -0.27 + x = -2.646677162 Solving -0.27 + x = -2.646677162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.27' to each side of the equation. -0.27 + 0.27 + x = -2.646677162 + 0.27 Combine like terms: -0.27 + 0.27 = 0.00 0.00 + x = -2.646677162 + 0.27 x = -2.646677162 + 0.27 Combine like terms: -2.646677162 + 0.27 = -2.376677162 x = -2.376677162 Simplifying x = -2.376677162Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.916677162, -2.376677162}
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