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Simplifying x2 + 0.4x = 62 Reorder the terms: 0.4x + x2 = 62 Solving 0.4x + x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + 0.4x + x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + 0.4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 0.4x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 0.4x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 0.4x + x2 = 0 + 62 0.4x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 0.4x + x2 = 62 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 62 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 62 + 0.04 Combine like terms: 62 + 0.04 = 62.04 0.04 + 0.4x + x2 = 62.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 62.04 Calculate the square root of the right side: 7.876547467 Break this problem into two subproblems by setting (x + 0.2) equal to 7.876547467 and -7.876547467.Subproblem 1
x + 0.2 = 7.876547467 Simplifying x + 0.2 = 7.876547467 Reorder the terms: 0.2 + x = 7.876547467 Solving 0.2 + x = 7.876547467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 7.876547467 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 7.876547467 + -0.2 x = 7.876547467 + -0.2 Combine like terms: 7.876547467 + -0.2 = 7.676547467 x = 7.676547467 Simplifying x = 7.676547467Subproblem 2
x + 0.2 = -7.876547467 Simplifying x + 0.2 = -7.876547467 Reorder the terms: 0.2 + x = -7.876547467 Solving 0.2 + x = -7.876547467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -7.876547467 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -7.876547467 + -0.2 x = -7.876547467 + -0.2 Combine like terms: -7.876547467 + -0.2 = -8.076547467 x = -8.076547467 Simplifying x = -8.076547467Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.676547467, -8.076547467}
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