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Simplifying 2x2 + 6x + -15x + 5 = 3x2 + 10x + 3 Reorder the terms: 5 + 6x + -15x + 2x2 = 3x2 + 10x + 3 Combine like terms: 6x + -15x = -9x 5 + -9x + 2x2 = 3x2 + 10x + 3 Reorder the terms: 5 + -9x + 2x2 = 3 + 10x + 3x2 Solving 5 + -9x + 2x2 = 3 + 10x + 3x2 Solving for variable 'x'. Reorder the terms: 5 + -3 + -9x + -10x + 2x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Combine like terms: 5 + -3 = 2 2 + -9x + -10x + 2x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Combine like terms: -9x + -10x = -19x 2 + -19x + 2x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 2 + -19x + -1x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Reorder the terms: 2 + -19x + -1x2 = 3 + -3 + 10x + -10x + 3x2 + -3x2 Combine like terms: 3 + -3 = 0 2 + -19x + -1x2 = 0 + 10x + -10x + 3x2 + -3x2 2 + -19x + -1x2 = 10x + -10x + 3x2 + -3x2 Combine like terms: 10x + -10x = 0 2 + -19x + -1x2 = 0 + 3x2 + -3x2 2 + -19x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 2 + -19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 19x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 19x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 19x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 19x + x2 = 0 + 2 19x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 19x + x2 = 2 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 2 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 2 + 90.25 Combine like terms: 2 + 90.25 = 92.25 90.25 + 19x + x2 = 92.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + 9.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + 9.5 = 9.604686356 Simplifying x + 9.5 = 9.604686356 Reorder the terms: 9.5 + x = 9.604686356 Solving 9.5 + x = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 9.604686356 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 9.604686356 + -9.5 x = 9.604686356 + -9.5 Combine like terms: 9.604686356 + -9.5 = 0.104686356 x = 0.104686356 Simplifying x = 0.104686356Subproblem 2
x + 9.5 = -9.604686356 Simplifying x + 9.5 = -9.604686356 Reorder the terms: 9.5 + x = -9.604686356 Solving 9.5 + x = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -9.604686356 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -9.604686356 + -9.5 x = -9.604686356 + -9.5 Combine like terms: -9.604686356 + -9.5 = -19.104686356 x = -19.104686356 Simplifying x = -19.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.104686356, -19.104686356}
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