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Simplifying 5x(2x + -3) = 3x + 13 Reorder the terms: 5x(-3 + 2x) = 3x + 13 (-3 * 5x + 2x * 5x) = 3x + 13 (-15x + 10x2) = 3x + 13 Reorder the terms: -15x + 10x2 = 13 + 3x Solving -15x + 10x2 = 13 + 3x Solving for variable 'x'. Reorder the terms: -13 + -15x + -3x + 10x2 = 13 + 3x + -13 + -3x Combine like terms: -15x + -3x = -18x -13 + -18x + 10x2 = 13 + 3x + -13 + -3x Reorder the terms: -13 + -18x + 10x2 = 13 + -13 + 3x + -3x Combine like terms: 13 + -13 = 0 -13 + -18x + 10x2 = 0 + 3x + -3x -13 + -18x + 10x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -13 + -18x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + -1.8x + x2 = 0.0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -1.8x + 1.3 + x2 = 0.0 + 1.3 Reorder the terms: -1.3 + 1.3 + -1.8x + x2 = 0.0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -1.8x + x2 = 0.0 + 1.3 -1.8x + x2 = 0.0 + 1.3 Combine like terms: 0.0 + 1.3 = 1.3 -1.8x + x2 = 1.3 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 1.3 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1.3 + 0.81 Combine like terms: 1.3 + 0.81 = 2.11 0.81 + -1.8x + x2 = 2.11 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 2.11 Calculate the square root of the right side: 1.452583905 Break this problem into two subproblems by setting (x + -0.9) equal to 1.452583905 and -1.452583905.Subproblem 1
x + -0.9 = 1.452583905 Simplifying x + -0.9 = 1.452583905 Reorder the terms: -0.9 + x = 1.452583905 Solving -0.9 + x = 1.452583905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.452583905 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.452583905 + 0.9 x = 1.452583905 + 0.9 Combine like terms: 1.452583905 + 0.9 = 2.352583905 x = 2.352583905 Simplifying x = 2.352583905Subproblem 2
x + -0.9 = -1.452583905 Simplifying x + -0.9 = -1.452583905 Reorder the terms: -0.9 + x = -1.452583905 Solving -0.9 + x = -1.452583905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.452583905 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.452583905 + 0.9 x = -1.452583905 + 0.9 Combine like terms: -1.452583905 + 0.9 = -0.552583905 x = -0.552583905 Simplifying x = -0.552583905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.352583905, -0.552583905}
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