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Simplifying 2x2 + 15x + -3 = 42 Reorder the terms: -3 + 15x + 2x2 = 42 Solving -3 + 15x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: -3 + -42 + 15x + 2x2 = 42 + -42 Combine like terms: -3 + -42 = -45 -45 + 15x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -45 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 7.5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 7.5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 7.5x + x2 = 0 + 22.5 7.5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 7.5x + x2 = 22.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 22.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 22.5 + 14.0625 Combine like terms: 22.5 + 14.0625 = 36.5625 14.0625 + 7.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + 3.75) equal to 6.046693311 and -6.046693311.Subproblem 1
x + 3.75 = 6.046693311 Simplifying x + 3.75 = 6.046693311 Reorder the terms: 3.75 + x = 6.046693311 Solving 3.75 + x = 6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 6.046693311 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 6.046693311 + -3.75 x = 6.046693311 + -3.75 Combine like terms: 6.046693311 + -3.75 = 2.296693311 x = 2.296693311 Simplifying x = 2.296693311Subproblem 2
x + 3.75 = -6.046693311 Simplifying x + 3.75 = -6.046693311 Reorder the terms: 3.75 + x = -6.046693311 Solving 3.75 + x = -6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -6.046693311 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -6.046693311 + -3.75 x = -6.046693311 + -3.75 Combine like terms: -6.046693311 + -3.75 = -9.796693311 x = -9.796693311 Simplifying x = -9.796693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.296693311, -9.796693311}
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