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Simplifying 5x2 + -20x = 62 Reorder the terms: -20x + 5x2 = 62 Solving -20x + 5x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + -20x + 5x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.4 + -4x + x2 = 0 Move the constant term to the right: Add '12.4' to each side of the equation. -12.4 + -4x + 12.4 + x2 = 0 + 12.4 Reorder the terms: -12.4 + 12.4 + -4x + x2 = 0 + 12.4 Combine like terms: -12.4 + 12.4 = 0.0 0.0 + -4x + x2 = 0 + 12.4 -4x + x2 = 0 + 12.4 Combine like terms: 0 + 12.4 = 12.4 -4x + x2 = 12.4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 12.4 + 4 Reorder the terms: 4 + -4x + x2 = 12.4 + 4 Combine like terms: 12.4 + 4 = 16.4 4 + -4x + x2 = 16.4 Factor a perfect square on the left side: (x + -2)(x + -2) = 16.4 Calculate the square root of the right side: 4.049691346 Break this problem into two subproblems by setting (x + -2) equal to 4.049691346 and -4.049691346.Subproblem 1
x + -2 = 4.049691346 Simplifying x + -2 = 4.049691346 Reorder the terms: -2 + x = 4.049691346 Solving -2 + x = 4.049691346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.049691346 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.049691346 + 2 x = 4.049691346 + 2 Combine like terms: 4.049691346 + 2 = 6.049691346 x = 6.049691346 Simplifying x = 6.049691346Subproblem 2
x + -2 = -4.049691346 Simplifying x + -2 = -4.049691346 Reorder the terms: -2 + x = -4.049691346 Solving -2 + x = -4.049691346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.049691346 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.049691346 + 2 x = -4.049691346 + 2 Combine like terms: -4.049691346 + 2 = -2.049691346 x = -2.049691346 Simplifying x = -2.049691346Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.049691346, -2.049691346}
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