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Simplifying 2x * 5(x + -3) = 13 Reorder the terms: 2x * 5(-3 + x) = 13 Reorder the terms for easier multiplication: 2 * 5x(-3 + x) = 13 Multiply 2 * 5 10x(-3 + x) = 13 (-3 * 10x + x * 10x) = 13 (-30x + 10x2) = 13 Solving -30x + 10x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -30x + 10x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -30x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + -3x + x2 = 0.0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -3x + 1.3 + x2 = 0.0 + 1.3 Reorder the terms: -1.3 + 1.3 + -3x + x2 = 0.0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -3x + x2 = 0.0 + 1.3 -3x + x2 = 0.0 + 1.3 Combine like terms: 0.0 + 1.3 = 1.3 -3x + x2 = 1.3 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 1.3 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1.3 + 2.25 Combine like terms: 1.3 + 2.25 = 3.55 2.25 + -3x + x2 = 3.55 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.55 Calculate the square root of the right side: 1.884144368 Break this problem into two subproblems by setting (x + -1.5) equal to 1.884144368 and -1.884144368.Subproblem 1
x + -1.5 = 1.884144368 Simplifying x + -1.5 = 1.884144368 Reorder the terms: -1.5 + x = 1.884144368 Solving -1.5 + x = 1.884144368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.884144368 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.884144368 + 1.5 x = 1.884144368 + 1.5 Combine like terms: 1.884144368 + 1.5 = 3.384144368 x = 3.384144368 Simplifying x = 3.384144368Subproblem 2
x + -1.5 = -1.884144368 Simplifying x + -1.5 = -1.884144368 Reorder the terms: -1.5 + x = -1.884144368 Solving -1.5 + x = -1.884144368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.884144368 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.884144368 + 1.5 x = -1.884144368 + 1.5 Combine like terms: -1.884144368 + 1.5 = -0.384144368 x = -0.384144368 Simplifying x = -0.384144368Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.384144368, -0.384144368}
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