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Simplifying 10x(x + 3) + -1(-9 + -4) = x + -5 + 3 Reorder the terms: 10x(3 + x) + -1(-9 + -4) = x + -5 + 3 (3 * 10x + x * 10x) + -1(-9 + -4) = x + -5 + 3 (30x + 10x2) + -1(-9 + -4) = x + -5 + 3 Combine like terms: -9 + -4 = -13 30x + 10x2 + -1(-13) = x + -5 + 3 Multiply -1 * -13 30x + 10x2 + 13 = x + -5 + 3 Reorder the terms: 13 + 30x + 10x2 = x + -5 + 3 Reorder the terms: 13 + 30x + 10x2 = -5 + 3 + x Combine like terms: -5 + 3 = -2 13 + 30x + 10x2 = -2 + x Solving 13 + 30x + 10x2 = -2 + x Solving for variable 'x'. Reorder the terms: 13 + 2 + 30x + -1x + 10x2 = -2 + x + 2 + -1x Combine like terms: 13 + 2 = 15 15 + 30x + -1x + 10x2 = -2 + x + 2 + -1x Combine like terms: 30x + -1x = 29x 15 + 29x + 10x2 = -2 + x + 2 + -1x Reorder the terms: 15 + 29x + 10x2 = -2 + 2 + x + -1x Combine like terms: -2 + 2 = 0 15 + 29x + 10x2 = 0 + x + -1x 15 + 29x + 10x2 = x + -1x Combine like terms: x + -1x = 0 15 + 29x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.5 + 2.9x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 2.9x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 2.9x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 2.9x + x2 = 0 + -1.5 2.9x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 2.9x + x2 = -1.5 The x term is 2.9x. Take half its coefficient (1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. 2.9x + 2.1025 + x2 = -1.5 + 2.1025 Reorder the terms: 2.1025 + 2.9x + x2 = -1.5 + 2.1025 Combine like terms: -1.5 + 2.1025 = 0.6025 2.1025 + 2.9x + x2 = 0.6025 Factor a perfect square on the left side: (x + 1.45)(x + 1.45) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + 1.45) equal to 0.776208735 and -0.776208735.Subproblem 1
x + 1.45 = 0.776208735 Simplifying x + 1.45 = 0.776208735 Reorder the terms: 1.45 + x = 0.776208735 Solving 1.45 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = 0.776208735 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = 0.776208735 + -1.45 x = 0.776208735 + -1.45 Combine like terms: 0.776208735 + -1.45 = -0.673791265 x = -0.673791265 Simplifying x = -0.673791265Subproblem 2
x + 1.45 = -0.776208735 Simplifying x + 1.45 = -0.776208735 Reorder the terms: 1.45 + x = -0.776208735 Solving 1.45 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + x = -0.776208735 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + x = -0.776208735 + -1.45 x = -0.776208735 + -1.45 Combine like terms: -0.776208735 + -1.45 = -2.226208735 x = -2.226208735 Simplifying x = -2.226208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.673791265, -2.226208735}
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