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Simplifying 3(x2 + 10x + -26) = 0 Reorder the terms: 3(-26 + 10x + x2) = 0 (-26 * 3 + 10x * 3 + x2 * 3) = 0 (-78 + 30x + 3x2) = 0 Solving -78 + 30x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-26 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-26 + 10x + x2)' equal to zero and attempt to solve: Simplifying -26 + 10x + x2 = 0 Solving -26 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 10x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 10x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 10x + x2 = 0 + 26 10x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 10x + x2 = 26 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 = 26 + 25 Reorder the terms: 25 + 10x + x2 = 26 + 25 Combine like terms: 26 + 25 = 51 25 + 10x + x2 = 51 Factor a perfect square on the left side: (x + 5)(x + 5) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + 5) equal to 7.141428429 and -7.141428429.Subproblem 1
x + 5 = 7.141428429 Simplifying x + 5 = 7.141428429 Reorder the terms: 5 + x = 7.141428429 Solving 5 + x = 7.141428429 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 = 7.141428429 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.141428429 + -5 x = 7.141428429 + -5 Combine like terms: 7.141428429 + -5 = 2.141428429 x = 2.141428429 Simplifying x = 2.141428429Subproblem 2
x + 5 = -7.141428429 Simplifying x + 5 = -7.141428429 Reorder the terms: 5 + x = -7.141428429 Solving 5 + x = -7.141428429 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 = -7.141428429 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.141428429 + -5 x = -7.141428429 + -5 Combine like terms: -7.141428429 + -5 = -12.141428429 x = -12.141428429 Simplifying x = -12.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.141428429, -12.141428429}Solution
x = {2.141428429, -12.141428429}
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