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Simplifying 7x + 42 + 6x = x2 + 6x Reorder the terms: 42 + 7x + 6x = x2 + 6x Combine like terms: 7x + 6x = 13x 42 + 13x = x2 + 6x Reorder the terms: 42 + 13x = 6x + x2 Solving 42 + 13x = 6x + x2 Solving for variable 'x'. Combine like terms: 13x + -6x = 7x 42 + 7x + -1x2 = 6x + x2 + -6x + -1x2 Reorder the terms: 42 + 7x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 42 + 7x + -1x2 = 0 + x2 + -1x2 42 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 42 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -42 + -7x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -7x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -7x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -7x + x2 = 0 + 42 -7x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -7x + x2 = 42 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 42 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 42 + 12.25 Combine like terms: 42 + 12.25 = 54.25 12.25 + -7x + x2 = 54.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + -3.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + -3.5 = 7.365459931 Simplifying x + -3.5 = 7.365459931 Reorder the terms: -3.5 + x = 7.365459931 Solving -3.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 7.365459931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.365459931 + 3.5 x = 7.365459931 + 3.5 Combine like terms: 7.365459931 + 3.5 = 10.865459931 x = 10.865459931 Simplifying x = 10.865459931Subproblem 2
x + -3.5 = -7.365459931 Simplifying x + -3.5 = -7.365459931 Reorder the terms: -3.5 + x = -7.365459931 Solving -3.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -7.365459931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.365459931 + 3.5 x = -7.365459931 + 3.5 Combine like terms: -7.365459931 + 3.5 = -3.865459931 x = -3.865459931 Simplifying x = -3.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.865459931, -3.865459931}
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