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Simplifying 10x2 + -4x = 18 + 7x2 Reorder the terms: -4x + 10x2 = 18 + 7x2 Solving -4x + 10x2 = 18 + 7x2 Solving for variable 'x'. Reorder the terms: -18 + -4x + 10x2 + -7x2 = 18 + 7x2 + -18 + -7x2 Combine like terms: 10x2 + -7x2 = 3x2 -18 + -4x + 3x2 = 18 + 7x2 + -18 + -7x2 Reorder the terms: -18 + -4x + 3x2 = 18 + -18 + 7x2 + -7x2 Combine like terms: 18 + -18 = 0 -18 + -4x + 3x2 = 0 + 7x2 + -7x2 -18 + -4x + 3x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -18 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.333333333x + x2 = 0 + 6 -1.333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.333333333x + x2 = 6 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 6 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 6 + 0.4444444442 Combine like terms: 6 + 0.4444444442 = 6.4444444442 0.4444444442 + -1.333333333x + x2 = 6.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 6.4444444442 Calculate the square root of the right side: 2.538591035 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.538591035 and -2.538591035.Subproblem 1
x + -0.6666666665 = 2.538591035 Simplifying x + -0.6666666665 = 2.538591035 Reorder the terms: -0.6666666665 + x = 2.538591035 Solving -0.6666666665 + x = 2.538591035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 2.538591035 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.538591035 + 0.6666666665 x = 2.538591035 + 0.6666666665 Combine like terms: 2.538591035 + 0.6666666665 = 3.2052577015 x = 3.2052577015 Simplifying x = 3.2052577015Subproblem 2
x + -0.6666666665 = -2.538591035 Simplifying x + -0.6666666665 = -2.538591035 Reorder the terms: -0.6666666665 + x = -2.538591035 Solving -0.6666666665 + x = -2.538591035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -2.538591035 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.538591035 + 0.6666666665 x = -2.538591035 + 0.6666666665 Combine like terms: -2.538591035 + 0.6666666665 = -1.8719243685 x = -1.8719243685 Simplifying x = -1.8719243685Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2052577015, -1.8719243685}
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