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Simplifying -1.5x2 + -15x + 42 = 0 Reorder the terms: 42 + -15x + -1.5x2 = 0 Solving 42 + -15x + -1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -28 + 10x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 10x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 10x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 10x + x2 = 0 + 28 10x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 10x + x2 = 28 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 28 + 25 Reorder the terms: 25 + 10x + x2 = 28 + 25 Combine like terms: 28 + 25 = 53 25 + 10x + x2 = 53 Factor a perfect square on the left side: (x + 5)(x + 5) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 5) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 5 = 7.280109889 Simplifying x + 5 = 7.280109889 Reorder the terms: 5 + x = 7.280109889 Solving 5 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.280109889 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.280109889 + -5 x = 7.280109889 + -5 Combine like terms: 7.280109889 + -5 = 2.280109889 x = 2.280109889 Simplifying x = 2.280109889Subproblem 2
x + 5 = -7.280109889 Simplifying x + 5 = -7.280109889 Reorder the terms: 5 + x = -7.280109889 Solving 5 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.280109889 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.280109889 + -5 x = -7.280109889 + -5 Combine like terms: -7.280109889 + -5 = -12.280109889 x = -12.280109889 Simplifying x = -12.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.280109889, -12.280109889}
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