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Simplifying 15x + -1x2 = 30 Solving 15x + -1x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 15x + -1x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -15x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -15x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -15x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -15x + x2 = 0 + -30 -15x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -15x + x2 = -30 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -30 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -30 + 56.25 Combine like terms: -30 + 56.25 = 26.25 56.25 + -15x + x2 = 26.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + -7.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + -7.5 = 5.123475383 Simplifying x + -7.5 = 5.123475383 Reorder the terms: -7.5 + x = 5.123475383 Solving -7.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.123475383 + 7.5 x = 5.123475383 + 7.5 Combine like terms: 5.123475383 + 7.5 = 12.623475383 x = 12.623475383 Simplifying x = 12.623475383Subproblem 2
x + -7.5 = -5.123475383 Simplifying x + -7.5 = -5.123475383 Reorder the terms: -7.5 + x = -5.123475383 Solving -7.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.123475383 + 7.5 x = -5.123475383 + 7.5 Combine like terms: -5.123475383 + 7.5 = 2.376524617 x = 2.376524617 Simplifying x = 2.376524617Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.623475383, 2.376524617}
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