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Simplifying 2x2 + 2x + 10 = 90 Reorder the terms: 10 + 2x + 2x2 = 90 Solving 10 + 2x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: 10 + -90 + 2x + 2x2 = 90 + -90 Combine like terms: 10 + -90 = -80 -80 + 2x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -80 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + x + x2)' equal to zero and attempt to solve: Simplifying -40 + x + x2 = 0 Solving -40 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + x + x2 = 0 + 40 x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 x + x2 = 40 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 40 + 0.25 Reorder the terms: 0.25 + x + x2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + x + x2 = 40.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 0.5 = 6.34428877 Simplifying x + 0.5 = 6.34428877 Reorder the terms: 0.5 + x = 6.34428877 Solving 0.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.34428877 + -0.5 x = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 x = 5.84428877 Simplifying x = 5.84428877Subproblem 2
x + 0.5 = -6.34428877 Simplifying x + 0.5 = -6.34428877 Reorder the terms: 0.5 + x = -6.34428877 Solving 0.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.34428877 + -0.5 x = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 x = -6.84428877 Simplifying x = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.84428877, -6.84428877}Solution
x = {5.84428877, -6.84428877}
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