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Simplifying x = 0.1x2 + 0.7x + -1.4 Reorder the terms: x = -1.4 + 0.7x + 0.1x2 Solving x = -1.4 + 0.7x + 0.1x2 Solving for variable 'x'. Reorder the terms: 1.4 + x + -0.7x + -0.1x2 = -1.4 + 0.7x + 0.1x2 + 1.4 + -0.7x + -0.1x2 Combine like terms: x + -0.7x = 0.3x 1.4 + 0.3x + -0.1x2 = -1.4 + 0.7x + 0.1x2 + 1.4 + -0.7x + -0.1x2 Reorder the terms: 1.4 + 0.3x + -0.1x2 = -1.4 + 1.4 + 0.7x + -0.7x + 0.1x2 + -0.1x2 Combine like terms: -1.4 + 1.4 = 0.0 1.4 + 0.3x + -0.1x2 = 0.0 + 0.7x + -0.7x + 0.1x2 + -0.1x2 1.4 + 0.3x + -0.1x2 = 0.7x + -0.7x + 0.1x2 + -0.1x2 Combine like terms: 0.7x + -0.7x = 0.0 1.4 + 0.3x + -0.1x2 = 0.0 + 0.1x2 + -0.1x2 1.4 + 0.3x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 1.4 + 0.3x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -14 + -3x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -3x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -3x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3x + x2 = 0 + 14 -3x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -3x + x2 = 14 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 14 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 14 + 2.25 Combine like terms: 14 + 2.25 = 16.25 2.25 + -3x + x2 = 16.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -1.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -1.5 = 4.031128874 Simplifying x + -1.5 = 4.031128874 Reorder the terms: -1.5 + x = 4.031128874 Solving -1.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.031128874 + 1.5 x = 4.031128874 + 1.5 Combine like terms: 4.031128874 + 1.5 = 5.531128874 x = 5.531128874 Simplifying x = 5.531128874Subproblem 2
x + -1.5 = -4.031128874 Simplifying x + -1.5 = -4.031128874 Reorder the terms: -1.5 + x = -4.031128874 Solving -1.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -4.031128874 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.031128874 + 1.5 x = -4.031128874 + 1.5 Combine like terms: -4.031128874 + 1.5 = -2.531128874 x = -2.531128874 Simplifying x = -2.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.531128874, -2.531128874}
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