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Simplifying 24x2 + 10x = 43 Reorder the terms: 10x + 24x2 = 43 Solving 10x + 24x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + 10x + 24x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 10x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.791666667 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '1.791666667' to each side of the equation. -1.791666667 + 0.4166666667x + 1.791666667 + x2 = 0 + 1.791666667 Reorder the terms: -1.791666667 + 1.791666667 + 0.4166666667x + x2 = 0 + 1.791666667 Combine like terms: -1.791666667 + 1.791666667 = 0.000000000 0.000000000 + 0.4166666667x + x2 = 0 + 1.791666667 0.4166666667x + x2 = 0 + 1.791666667 Combine like terms: 0 + 1.791666667 = 1.791666667 0.4166666667x + x2 = 1.791666667 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 = 1.791666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 1.791666667 + 0.04340277781 Combine like terms: 1.791666667 + 0.04340277781 = 1.83506944481 0.04340277781 + 0.4166666667x + x2 = 1.83506944481 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 1.83506944481 Calculate the square root of the right side: 1.354647351 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 1.354647351 and -1.354647351.Subproblem 1
x + 0.2083333334 = 1.354647351 Simplifying x + 0.2083333334 = 1.354647351 Reorder the terms: 0.2083333334 + x = 1.354647351 Solving 0.2083333334 + x = 1.354647351 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 = 1.354647351 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 1.354647351 + -0.2083333334 x = 1.354647351 + -0.2083333334 Combine like terms: 1.354647351 + -0.2083333334 = 1.1463140176 x = 1.1463140176 Simplifying x = 1.1463140176Subproblem 2
x + 0.2083333334 = -1.354647351 Simplifying x + 0.2083333334 = -1.354647351 Reorder the terms: 0.2083333334 + x = -1.354647351 Solving 0.2083333334 + x = -1.354647351 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 = -1.354647351 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -1.354647351 + -0.2083333334 x = -1.354647351 + -0.2083333334 Combine like terms: -1.354647351 + -0.2083333334 = -1.5629806844 x = -1.5629806844 Simplifying x = -1.5629806844Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1463140176, -1.5629806844}
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