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Simplifying 0.4x2 + -5x + 4.9 = 5x Reorder the terms: 4.9 + -5x + 0.4x2 = 5x Solving 4.9 + -5x + 0.4x2 = 5x Solving for variable 'x'. Reorder the terms: 4.9 + -5x + -5x + 0.4x2 = 5x + -5x Combine like terms: -5x + -5x = -10x 4.9 + -10x + 0.4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 4.9 + -10x + 0.4x2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 12.25 + -25x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -25x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -25x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -25x + x2 = 0 + -12.25 -25x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -25x + x2 = -12.25 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -12.25 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -12.25 + 156.25 Combine like terms: -12.25 + 156.25 = 144 156.25 + -25x + x2 = 144 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -12.5) equal to 12 and -12.Subproblem 1
x + -12.5 = 12 Simplifying x + -12.5 = 12 Reorder the terms: -12.5 + x = 12 Solving -12.5 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12 + 12.5 x = 12 + 12.5 Combine like terms: 12 + 12.5 = 24.5 x = 24.5 Simplifying x = 24.5Subproblem 2
x + -12.5 = -12 Simplifying x + -12.5 = -12 Reorder the terms: -12.5 + x = -12 Solving -12.5 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12 + 12.5 x = -12 + 12.5 Combine like terms: -12 + 12.5 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.5, 0.5}
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