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Simplifying 0 = x2 + 20x + 70 Reorder the terms: 0 = 70 + 20x + x2 Solving 0 = 70 + 20x + x2 Solving for variable 'x'. Combine like terms: 0 + -70 = -70 -70 + -20x + -1x2 = 70 + 20x + x2 + -70 + -20x + -1x2 Reorder the terms: -70 + -20x + -1x2 = 70 + -70 + 20x + -20x + x2 + -1x2 Combine like terms: 70 + -70 = 0 -70 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 -70 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 -70 + -20x + -1x2 = 0 + x2 + -1x2 -70 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -70 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(70 + 20x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(70 + 20x + x2)' equal to zero and attempt to solve: Simplifying 70 + 20x + x2 = 0 Solving 70 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + 20x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + 20x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + 20x + x2 = 0 + -70 20x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 20x + x2 = -70 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -70 + 100 Reorder the terms: 100 + 20x + x2 = -70 + 100 Combine like terms: -70 + 100 = 30 100 + 20x + x2 = 30 Factor a perfect square on the left side: (x + 10)(x + 10) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 10) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 10 = 5.477225575 Simplifying x + 10 = 5.477225575 Reorder the terms: 10 + x = 5.477225575 Solving 10 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 5.477225575 + -10 Combine like terms: 10 + -10 = 0 0 + x = 5.477225575 + -10 x = 5.477225575 + -10 Combine like terms: 5.477225575 + -10 = -4.522774425 x = -4.522774425 Simplifying x = -4.522774425Subproblem 2
x + 10 = -5.477225575 Simplifying x + 10 = -5.477225575 Reorder the terms: 10 + x = -5.477225575 Solving 10 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -5.477225575 + -10 Combine like terms: 10 + -10 = 0 0 + x = -5.477225575 + -10 x = -5.477225575 + -10 Combine like terms: -5.477225575 + -10 = -15.477225575 x = -15.477225575 Simplifying x = -15.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.522774425, -15.477225575}Solution
x = {-4.522774425, -15.477225575}
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