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Simplifying 61x2 + 20x + 4 = 90 Reorder the terms: 4 + 20x + 61x2 = 90 Solving 4 + 20x + 61x2 = 90 Solving for variable 'x'. Reorder the terms: 4 + -90 + 20x + 61x2 = 90 + -90 Combine like terms: 4 + -90 = -86 -86 + 20x + 61x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -86 + 20x + 61x2 = 0 Begin completing the square. Divide all terms by 61 the coefficient of the squared term: Divide each side by '61'. -1.409836066 + 0.3278688525x + x2 = 0 Move the constant term to the right: Add '1.409836066' to each side of the equation. -1.409836066 + 0.3278688525x + 1.409836066 + x2 = 0 + 1.409836066 Reorder the terms: -1.409836066 + 1.409836066 + 0.3278688525x + x2 = 0 + 1.409836066 Combine like terms: -1.409836066 + 1.409836066 = 0.000000000 0.000000000 + 0.3278688525x + x2 = 0 + 1.409836066 0.3278688525x + x2 = 0 + 1.409836066 Combine like terms: 0 + 1.409836066 = 1.409836066 0.3278688525x + x2 = 1.409836066 The x term is 0.3278688525x. Take half its coefficient (0.1639344263). Square it (0.02687449613) and add it to both sides. Add '0.02687449613' to each side of the equation. 0.3278688525x + 0.02687449613 + x2 = 1.409836066 + 0.02687449613 Reorder the terms: 0.02687449613 + 0.3278688525x + x2 = 1.409836066 + 0.02687449613 Combine like terms: 1.409836066 + 0.02687449613 = 1.43671056213 0.02687449613 + 0.3278688525x + x2 = 1.43671056213 Factor a perfect square on the left side: (x + 0.1639344263)(x + 0.1639344263) = 1.43671056213 Calculate the square root of the right side: 1.198628617 Break this problem into two subproblems by setting (x + 0.1639344263) equal to 1.198628617 and -1.198628617.Subproblem 1
x + 0.1639344263 = 1.198628617 Simplifying x + 0.1639344263 = 1.198628617 Reorder the terms: 0.1639344263 + x = 1.198628617 Solving 0.1639344263 + x = 1.198628617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1639344263' to each side of the equation. 0.1639344263 + -0.1639344263 + x = 1.198628617 + -0.1639344263 Combine like terms: 0.1639344263 + -0.1639344263 = 0.0000000000 0.0000000000 + x = 1.198628617 + -0.1639344263 x = 1.198628617 + -0.1639344263 Combine like terms: 1.198628617 + -0.1639344263 = 1.0346941907 x = 1.0346941907 Simplifying x = 1.0346941907Subproblem 2
x + 0.1639344263 = -1.198628617 Simplifying x + 0.1639344263 = -1.198628617 Reorder the terms: 0.1639344263 + x = -1.198628617 Solving 0.1639344263 + x = -1.198628617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1639344263' to each side of the equation. 0.1639344263 + -0.1639344263 + x = -1.198628617 + -0.1639344263 Combine like terms: 0.1639344263 + -0.1639344263 = 0.0000000000 0.0000000000 + x = -1.198628617 + -0.1639344263 x = -1.198628617 + -0.1639344263 Combine like terms: -1.198628617 + -0.1639344263 = -1.3625630433 x = -1.3625630433 Simplifying x = -1.3625630433Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0346941907, -1.3625630433}
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