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Simplifying x + 2x(2x + -4) = 51 Reorder the terms: x + 2x(-4 + 2x) = 51 x + (-4 * 2x + 2x * 2x) = 51 x + (-8x + 4x2) = 51 Combine like terms: x + -8x = -7x -7x + 4x2 = 51 Solving -7x + 4x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + -7x + 4x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + -1.75x + 12.75 + x2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + -1.75x + x2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + -1.75x + x2 = 0 + 12.75 -1.75x + x2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 -1.75x + x2 = 12.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 12.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 12.75 + 0.765625 Combine like terms: 12.75 + 0.765625 = 13.515625 0.765625 + -1.75x + x2 = 13.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 13.515625 Calculate the square root of the right side: 3.676360292 Break this problem into two subproblems by setting (x + -0.875) equal to 3.676360292 and -3.676360292.Subproblem 1
x + -0.875 = 3.676360292 Simplifying x + -0.875 = 3.676360292 Reorder the terms: -0.875 + x = 3.676360292 Solving -0.875 + x = 3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 3.676360292 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 3.676360292 + 0.875 x = 3.676360292 + 0.875 Combine like terms: 3.676360292 + 0.875 = 4.551360292 x = 4.551360292 Simplifying x = 4.551360292Subproblem 2
x + -0.875 = -3.676360292 Simplifying x + -0.875 = -3.676360292 Reorder the terms: -0.875 + x = -3.676360292 Solving -0.875 + x = -3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -3.676360292 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -3.676360292 + 0.875 x = -3.676360292 + 0.875 Combine like terms: -3.676360292 + 0.875 = -2.801360292 x = -2.801360292 Simplifying x = -2.801360292Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.551360292, -2.801360292}
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