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Simplifying 12x * x + 5x + 4 = 125 Multiply x * x 12x2 + 5x + 4 = 125 Reorder the terms: 4 + 5x + 12x2 = 125 Solving 4 + 5x + 12x2 = 125 Solving for variable 'x'. Reorder the terms: 4 + -125 + 5x + 12x2 = 125 + -125 Combine like terms: 4 + -125 = -121 -121 + 5x + 12x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -121 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -10.08333333 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '10.08333333' to each side of the equation. -10.08333333 + 0.4166666667x + 10.08333333 + x2 = 0 + 10.08333333 Reorder the terms: -10.08333333 + 10.08333333 + 0.4166666667x + x2 = 0 + 10.08333333 Combine like terms: -10.08333333 + 10.08333333 = 0.00000000 0.00000000 + 0.4166666667x + x2 = 0 + 10.08333333 0.4166666667x + x2 = 0 + 10.08333333 Combine like terms: 0 + 10.08333333 = 10.08333333 0.4166666667x + x2 = 10.08333333 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 10.08333333 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 10.08333333 + 0.04340277781 Combine like terms: 10.08333333 + 0.04340277781 = 10.12673610781 0.04340277781 + 0.4166666667x + x2 = 10.12673610781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 10.12673610781 Calculate the square root of the right side: 3.182253307 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 3.182253307 and -3.182253307.Subproblem 1
x + 0.2083333334 = 3.182253307 Simplifying x + 0.2083333334 = 3.182253307 Reorder the terms: 0.2083333334 + x = 3.182253307 Solving 0.2083333334 + x = 3.182253307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 3.182253307 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 3.182253307 + -0.2083333334 x = 3.182253307 + -0.2083333334 Combine like terms: 3.182253307 + -0.2083333334 = 2.9739199736 x = 2.9739199736 Simplifying x = 2.9739199736Subproblem 2
x + 0.2083333334 = -3.182253307 Simplifying x + 0.2083333334 = -3.182253307 Reorder the terms: 0.2083333334 + x = -3.182253307 Solving 0.2083333334 + x = -3.182253307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -3.182253307 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -3.182253307 + -0.2083333334 x = -3.182253307 + -0.2083333334 Combine like terms: -3.182253307 + -0.2083333334 = -3.3905866404 x = -3.3905866404 Simplifying x = -3.3905866404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9739199736, -3.3905866404}
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