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Simplifying 5x(3x + -29) = 69 Reorder the terms: 5x(-29 + 3x) = 69 (-29 * 5x + 3x * 5x) = 69 (-145x + 15x2) = 69 Solving -145x + 15x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + -145x + 15x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + -145x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4.6 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -9.666666667x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -9.666666667x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -9.666666667x + x2 = 0 + 4.6 -9.666666667x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -9.666666667x + x2 = 4.6 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 = 4.6 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = 4.6 + 23.36111112 Combine like terms: 4.6 + 23.36111112 = 27.96111112 23.36111112 + -9.666666667x + x2 = 27.96111112 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 27.96111112 Calculate the square root of the right side: 5.287826692 Break this problem into two subproblems by setting (x + -4.833333334) equal to 5.287826692 and -5.287826692.Subproblem 1
x + -4.833333334 = 5.287826692 Simplifying x + -4.833333334 = 5.287826692 Reorder the terms: -4.833333334 + x = 5.287826692 Solving -4.833333334 + x = 5.287826692 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 = 5.287826692 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 5.287826692 + 4.833333334 x = 5.287826692 + 4.833333334 Combine like terms: 5.287826692 + 4.833333334 = 10.121160026 x = 10.121160026 Simplifying x = 10.121160026Subproblem 2
x + -4.833333334 = -5.287826692 Simplifying x + -4.833333334 = -5.287826692 Reorder the terms: -4.833333334 + x = -5.287826692 Solving -4.833333334 + x = -5.287826692 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 = -5.287826692 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -5.287826692 + 4.833333334 x = -5.287826692 + 4.833333334 Combine like terms: -5.287826692 + 4.833333334 = -0.454493358 x = -0.454493358 Simplifying x = -0.454493358Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.121160026, -0.454493358}
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