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Simplifying x = 3x2 + -28x + 45 Reorder the terms: x = 45 + -28x + 3x2 Solving x = 45 + -28x + 3x2 Solving for variable 'x'. Reorder the terms: -45 + x + 28x + -3x2 = 45 + -28x + 3x2 + -45 + 28x + -3x2 Combine like terms: x + 28x = 29x -45 + 29x + -3x2 = 45 + -28x + 3x2 + -45 + 28x + -3x2 Reorder the terms: -45 + 29x + -3x2 = 45 + -45 + -28x + 28x + 3x2 + -3x2 Combine like terms: 45 + -45 = 0 -45 + 29x + -3x2 = 0 + -28x + 28x + 3x2 + -3x2 -45 + 29x + -3x2 = -28x + 28x + 3x2 + -3x2 Combine like terms: -28x + 28x = 0 -45 + 29x + -3x2 = 0 + 3x2 + -3x2 -45 + 29x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -45 + 29x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 15 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -9.666666667x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -9.666666667x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -9.666666667x + x2 = 0 + -15 -9.666666667x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -9.666666667x + x2 = -15 The x term is -9.666666667x. Take half its coefficient (-4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. -9.666666667x + 23.36111112 + x2 = -15 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = -15 + 23.36111112 Combine like terms: -15 + 23.36111112 = 8.36111112 23.36111112 + -9.666666667x + x2 = 8.36111112 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 8.36111112 Calculate the square root of the right side: 2.891558597 Break this problem into two subproblems by setting (x + -4.833333334) equal to 2.891558597 and -2.891558597.Subproblem 1
x + -4.833333334 = 2.891558597 Simplifying x + -4.833333334 = 2.891558597 Reorder the terms: -4.833333334 + x = 2.891558597 Solving -4.833333334 + x = 2.891558597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = 2.891558597 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 2.891558597 + 4.833333334 x = 2.891558597 + 4.833333334 Combine like terms: 2.891558597 + 4.833333334 = 7.724891931 x = 7.724891931 Simplifying x = 7.724891931Subproblem 2
x + -4.833333334 = -2.891558597 Simplifying x + -4.833333334 = -2.891558597 Reorder the terms: -4.833333334 + x = -2.891558597 Solving -4.833333334 + x = -2.891558597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = -2.891558597 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -2.891558597 + 4.833333334 x = -2.891558597 + 4.833333334 Combine like terms: -2.891558597 + 4.833333334 = 1.941774737 x = 1.941774737 Simplifying x = 1.941774737Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.724891931, 1.941774737}
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