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Simplifying 5 + 2(x + 1) + -3 = -2(x + -3) * 4x Reorder the terms: 5 + 2(1 + x) + -3 = -2(x + -3) * 4x 5 + (1 * 2 + x * 2) + -3 = -2(x + -3) * 4x 5 + (2 + 2x) + -3 = -2(x + -3) * 4x Reorder the terms: 5 + 2 + -3 + 2x = -2(x + -3) * 4x Combine like terms: 5 + 2 = 7 7 + -3 + 2x = -2(x + -3) * 4x Combine like terms: 7 + -3 = 4 4 + 2x = -2(x + -3) * 4x Reorder the terms: 4 + 2x = -2(-3 + x) * 4x Reorder the terms for easier multiplication: 4 + 2x = -2 * 4x(-3 + x) Multiply -2 * 4 4 + 2x = -8x(-3 + x) 4 + 2x = (-3 * -8x + x * -8x) 4 + 2x = (24x + -8x2) Solving 4 + 2x = 24x + -8x2 Solving for variable 'x'. Combine like terms: 2x + -24x = -22x 4 + -22x + 8x2 = 24x + -8x2 + -24x + 8x2 Reorder the terms: 4 + -22x + 8x2 = 24x + -24x + -8x2 + 8x2 Combine like terms: 24x + -24x = 0 4 + -22x + 8x2 = 0 + -8x2 + 8x2 4 + -22x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 4 + -22x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -11x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -11x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + -11x + 4x2 = 0 Solving 2 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2.75x + x2 = 0 + -0.5 -2.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2.75x + x2 = -0.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = -0.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = -0.5 + 1.890625 Combine like terms: -0.5 + 1.890625 = 1.390625 1.890625 + -2.75x + x2 = 1.390625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -1.375) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -1.375 = 1.179247642 Simplifying x + -1.375 = 1.179247642 Reorder the terms: -1.375 + x = 1.179247642 Solving -1.375 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.179247642 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.179247642 + 1.375 x = 1.179247642 + 1.375 Combine like terms: 1.179247642 + 1.375 = 2.554247642 x = 2.554247642 Simplifying x = 2.554247642Subproblem 2
x + -1.375 = -1.179247642 Simplifying x + -1.375 = -1.179247642 Reorder the terms: -1.375 + x = -1.179247642 Solving -1.375 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.179247642 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.179247642 + 1.375 x = -1.179247642 + 1.375 Combine like terms: -1.179247642 + 1.375 = 0.195752358 x = 0.195752358 Simplifying x = 0.195752358Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.554247642, 0.195752358}Solution
x = {2.554247642, 0.195752358}
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