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Simplifying 3x + 5 = 5x2 + 2(x + -4) Reorder the terms: 5 + 3x = 5x2 + 2(x + -4) Reorder the terms: 5 + 3x = 5x2 + 2(-4 + x) 5 + 3x = 5x2 + (-4 * 2 + x * 2) 5 + 3x = 5x2 + (-8 + 2x) Reorder the terms: 5 + 3x = -8 + 2x + 5x2 Solving 5 + 3x = -8 + 2x + 5x2 Solving for variable 'x'. Reorder the terms: 5 + 8 + 3x + -2x + -5x2 = -8 + 2x + 5x2 + 8 + -2x + -5x2 Combine like terms: 5 + 8 = 13 13 + 3x + -2x + -5x2 = -8 + 2x + 5x2 + 8 + -2x + -5x2 Combine like terms: 3x + -2x = 1x 13 + 1x + -5x2 = -8 + 2x + 5x2 + 8 + -2x + -5x2 Reorder the terms: 13 + 1x + -5x2 = -8 + 8 + 2x + -2x + 5x2 + -5x2 Combine like terms: -8 + 8 = 0 13 + 1x + -5x2 = 0 + 2x + -2x + 5x2 + -5x2 13 + 1x + -5x2 = 2x + -2x + 5x2 + -5x2 Combine like terms: 2x + -2x = 0 13 + 1x + -5x2 = 0 + 5x2 + -5x2 13 + 1x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 13 + 1x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.6 + -0.2x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -0.2x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -0.2x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -0.2x + x2 = 0 + 2.6 -0.2x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -0.2x + x2 = 2.6 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 2.6 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 2.6 + 0.01 Combine like terms: 2.6 + 0.01 = 2.61 0.01 + -0.2x + x2 = 2.61 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 2.61 Calculate the square root of the right side: 1.615549442 Break this problem into two subproblems by setting (x + -0.1) equal to 1.615549442 and -1.615549442.Subproblem 1
x + -0.1 = 1.615549442 Simplifying x + -0.1 = 1.615549442 Reorder the terms: -0.1 + x = 1.615549442 Solving -0.1 + x = 1.615549442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.615549442 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.615549442 + 0.1 x = 1.615549442 + 0.1 Combine like terms: 1.615549442 + 0.1 = 1.715549442 x = 1.715549442 Simplifying x = 1.715549442Subproblem 2
x + -0.1 = -1.615549442 Simplifying x + -0.1 = -1.615549442 Reorder the terms: -0.1 + x = -1.615549442 Solving -0.1 + x = -1.615549442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.615549442 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.615549442 + 0.1 x = -1.615549442 + 0.1 Combine like terms: -1.615549442 + 0.1 = -1.515549442 x = -1.515549442 Simplifying x = -1.515549442Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.715549442, -1.515549442}
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