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Simplifying 2x * 4 + -1x + 7 + 4x + -8 + -5x2 + 2 + 3x = 0 Reorder the terms for easier multiplication: 2 * 4x + -1x + 7 + 4x + -8 + -5x2 + 2 + 3x = 0 Multiply 2 * 4 8x + -1x + 7 + 4x + -8 + -5x2 + 2 + 3x = 0 Reorder the terms: 7 + -8 + 2 + 8x + -1x + 4x + 3x + -5x2 = 0 Combine like terms: 7 + -8 = -1 -1 + 2 + 8x + -1x + 4x + 3x + -5x2 = 0 Combine like terms: -1 + 2 = 1 1 + 8x + -1x + 4x + 3x + -5x2 = 0 Combine like terms: 8x + -1x = 7x 1 + 7x + 4x + 3x + -5x2 = 0 Combine like terms: 7x + 4x = 11x 1 + 11x + 3x + -5x2 = 0 Combine like terms: 11x + 3x = 14x 1 + 14x + -5x2 = 0 Solving 1 + 14x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -2.8x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2.8x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2.8x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2.8x + x2 = 0 + 0.2 -2.8x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2.8x + x2 = 0.2 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 0.2 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 0.2 + 1.96 Combine like terms: 0.2 + 1.96 = 2.16 1.96 + -2.8x + x2 = 2.16 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + -1.4) equal to 1.469693846 and -1.469693846.Subproblem 1
x + -1.4 = 1.469693846 Simplifying x + -1.4 = 1.469693846 Reorder the terms: -1.4 + x = 1.469693846 Solving -1.4 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.469693846 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.469693846 + 1.4 x = 1.469693846 + 1.4 Combine like terms: 1.469693846 + 1.4 = 2.869693846 x = 2.869693846 Simplifying x = 2.869693846Subproblem 2
x + -1.4 = -1.469693846 Simplifying x + -1.4 = -1.469693846 Reorder the terms: -1.4 + x = -1.469693846 Solving -1.4 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.469693846 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.469693846 + 1.4 x = -1.469693846 + 1.4 Combine like terms: -1.469693846 + 1.4 = -0.069693846 x = -0.069693846 Simplifying x = -0.069693846Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.869693846, -0.069693846}
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