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Simplifying 25x2 + -20x = 4 Reorder the terms: -20x + 25x2 = 4 Solving -20x + 25x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -20x + 25x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.8x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.8x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.8x + x2 = 0 + 0.16 -0.8x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.8x + x2 = 0.16 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.16 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.16 + 0.16 Combine like terms: 0.16 + 0.16 = 0.32 0.16 + -0.8x + x2 = 0.32 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.32 Calculate the square root of the right side: 0.565685425 Break this problem into two subproblems by setting (x + -0.4) equal to 0.565685425 and -0.565685425.Subproblem 1
x + -0.4 = 0.565685425 Simplifying x + -0.4 = 0.565685425 Reorder the terms: -0.4 + x = 0.565685425 Solving -0.4 + x = 0.565685425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.565685425 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.565685425 + 0.4 x = 0.565685425 + 0.4 Combine like terms: 0.565685425 + 0.4 = 0.965685425 x = 0.965685425 Simplifying x = 0.965685425Subproblem 2
x + -0.4 = -0.565685425 Simplifying x + -0.4 = -0.565685425 Reorder the terms: -0.4 + x = -0.565685425 Solving -0.4 + x = -0.565685425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.565685425 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.565685425 + 0.4 x = -0.565685425 + 0.4 Combine like terms: -0.565685425 + 0.4 = -0.165685425 x = -0.165685425 Simplifying x = -0.165685425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.965685425, -0.165685425}
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