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Simplifying 12x2 + 5x = 84 Reorder the terms: 5x + 12x2 = 84 Solving 5x + 12x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 5x + 12x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -7 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.4166666667x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 0.4166666667x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.4166666667x + x2 = 0 + 7 0.4166666667x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.4166666667x + x2 = 7 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 = 7 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 7 + 0.04340277781 Combine like terms: 7 + 0.04340277781 = 7.04340277781 0.04340277781 + 0.4166666667x + x2 = 7.04340277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 7.04340277781 Calculate the square root of the right side: 2.65394099 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 2.65394099 and -2.65394099.Subproblem 1
x + 0.2083333334 = 2.65394099 Simplifying x + 0.2083333334 = 2.65394099 Reorder the terms: 0.2083333334 + x = 2.65394099 Solving 0.2083333334 + x = 2.65394099 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 = 2.65394099 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 2.65394099 + -0.2083333334 x = 2.65394099 + -0.2083333334 Combine like terms: 2.65394099 + -0.2083333334 = 2.4456076566 x = 2.4456076566 Simplifying x = 2.4456076566Subproblem 2
x + 0.2083333334 = -2.65394099 Simplifying x + 0.2083333334 = -2.65394099 Reorder the terms: 0.2083333334 + x = -2.65394099 Solving 0.2083333334 + x = -2.65394099 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 = -2.65394099 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -2.65394099 + -0.2083333334 x = -2.65394099 + -0.2083333334 Combine like terms: -2.65394099 + -0.2083333334 = -2.8622743234 x = -2.8622743234 Simplifying x = -2.8622743234Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4456076566, -2.8622743234}
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