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Simplifying 5x2 + 10x + -105 = 0 Reorder the terms: -105 + 10x + 5x2 = 0 Solving -105 + 10x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-21 + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-21 + 2x + x2)' equal to zero and attempt to solve: Simplifying -21 + 2x + x2 = 0 Solving -21 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 2x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 2x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x + x2 = 0 + 21 2x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 2x + x2 = 21 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 = 21 + 1 Reorder the terms: 1 + 2x + x2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + 2x + x2 = 22 Factor a perfect square on the left side: (x + 1)(x + 1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 1) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 1 = 4.69041576 Simplifying x + 1 = 4.69041576 Reorder the terms: 1 + x = 4.69041576 Solving 1 + x = 4.69041576 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 = 4.69041576 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.69041576 + -1 x = 4.69041576 + -1 Combine like terms: 4.69041576 + -1 = 3.69041576 x = 3.69041576 Simplifying x = 3.69041576Subproblem 2
x + 1 = -4.69041576 Simplifying x + 1 = -4.69041576 Reorder the terms: 1 + x = -4.69041576 Solving 1 + x = -4.69041576 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 = -4.69041576 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.69041576 + -1 x = -4.69041576 + -1 Combine like terms: -4.69041576 + -1 = -5.69041576 x = -5.69041576 Simplifying x = -5.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.69041576, -5.69041576}Solution
x = {3.69041576, -5.69041576}
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