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Simplifying 3x2 + 5x + -20 = 10 + -1x Reorder the terms: -20 + 5x + 3x2 = 10 + -1x Solving -20 + 5x + 3x2 = 10 + -1x Solving for variable 'x'. Reorder the terms: -20 + -10 + 5x + x + 3x2 = 10 + -1x + -10 + x Combine like terms: -20 + -10 = -30 -30 + 5x + x + 3x2 = 10 + -1x + -10 + x Combine like terms: 5x + x = 6x -30 + 6x + 3x2 = 10 + -1x + -10 + x Reorder the terms: -30 + 6x + 3x2 = 10 + -10 + -1x + x Combine like terms: 10 + -10 = 0 -30 + 6x + 3x2 = 0 + -1x + x -30 + 6x + 3x2 = -1x + x Combine like terms: -1x + x = 0 -30 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 2x + x2)' equal to zero and attempt to solve: Simplifying -10 + 2x + x2 = 0 Solving -10 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2x + x2 = 0 + 10 2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2x + x2 = 10 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10 + 1 Reorder the terms: 1 + 2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2x + x2 = 11 Factor a perfect square on the left side: (x + 1)(x + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 1 = 3.31662479 Simplifying x + 1 = 3.31662479 Reorder the terms: 1 + x = 3.31662479 Solving 1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.31662479 + -1 x = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 x = 2.31662479 Simplifying x = 2.31662479Subproblem 2
x + 1 = -3.31662479 Simplifying x + 1 = -3.31662479 Reorder the terms: 1 + x = -3.31662479 Solving 1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.31662479 + -1 x = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 x = -4.31662479 Simplifying x = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31662479, -4.31662479}Solution
x = {2.31662479, -4.31662479}
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