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Simplifying 2(4x + -2) * x = 16 + -1x Reorder the terms: 2(-2 + 4x) * x = 16 + -1x Reorder the terms for easier multiplication: 2x(-2 + 4x) = 16 + -1x (-2 * 2x + 4x * 2x) = 16 + -1x (-4x + 8x2) = 16 + -1x Solving -4x + 8x2 = 16 + -1x Solving for variable 'x'. Reorder the terms: -16 + -4x + x + 8x2 = 16 + -1x + -16 + x Combine like terms: -4x + x = -3x -16 + -3x + 8x2 = 16 + -1x + -16 + x Reorder the terms: -16 + -3x + 8x2 = 16 + -16 + -1x + x Combine like terms: 16 + -16 = 0 -16 + -3x + 8x2 = 0 + -1x + x -16 + -3x + 8x2 = -1x + x Combine like terms: -1x + x = 0 -16 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2 + -0.375x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.375x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.375x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.375x + x2 = 0 + 2 -0.375x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.375x + x2 = 2 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 2 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 2 + 0.03515625 Combine like terms: 2 + 0.03515625 = 2.03515625 0.03515625 + -0.375x + x2 = 2.03515625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 2.03515625 Calculate the square root of the right side: 1.426589026 Break this problem into two subproblems by setting (x + -0.1875) equal to 1.426589026 and -1.426589026.Subproblem 1
x + -0.1875 = 1.426589026 Simplifying x + -0.1875 = 1.426589026 Reorder the terms: -0.1875 + x = 1.426589026 Solving -0.1875 + x = 1.426589026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.426589026 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.426589026 + 0.1875 x = 1.426589026 + 0.1875 Combine like terms: 1.426589026 + 0.1875 = 1.614089026 x = 1.614089026 Simplifying x = 1.614089026Subproblem 2
x + -0.1875 = -1.426589026 Simplifying x + -0.1875 = -1.426589026 Reorder the terms: -0.1875 + x = -1.426589026 Solving -0.1875 + x = -1.426589026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.426589026 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.426589026 + 0.1875 x = -1.426589026 + 0.1875 Combine like terms: -1.426589026 + 0.1875 = -1.239089026 x = -1.239089026 Simplifying x = -1.239089026Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.614089026, -1.239089026}
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