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Simplifying 25x2 + 4x + -12 = 0 Reorder the terms: -12 + 4x + 25x2 = 0 Solving -12 + 4x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + 0.16x + x2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + 0.16x + 0.48 + x2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + 0.16x + x2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + 0.16x + x2 = 0 + 0.48 0.16x + x2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 0.16x + x2 = 0.48 The x term is 0.16x. Take half its coefficient (0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. 0.16x + 0.0064 + x2 = 0.48 + 0.0064 Reorder the terms: 0.0064 + 0.16x + x2 = 0.48 + 0.0064 Combine like terms: 0.48 + 0.0064 = 0.4864 0.0064 + 0.16x + x2 = 0.4864 Factor a perfect square on the left side: (x + 0.08)(x + 0.08) = 0.4864 Calculate the square root of the right side: 0.697423831 Break this problem into two subproblems by setting (x + 0.08) equal to 0.697423831 and -0.697423831.Subproblem 1
x + 0.08 = 0.697423831 Simplifying x + 0.08 = 0.697423831 Reorder the terms: 0.08 + x = 0.697423831 Solving 0.08 + x = 0.697423831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = 0.697423831 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = 0.697423831 + -0.08 x = 0.697423831 + -0.08 Combine like terms: 0.697423831 + -0.08 = 0.617423831 x = 0.617423831 Simplifying x = 0.617423831Subproblem 2
x + 0.08 = -0.697423831 Simplifying x + 0.08 = -0.697423831 Reorder the terms: 0.08 + x = -0.697423831 Solving 0.08 + x = -0.697423831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = -0.697423831 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = -0.697423831 + -0.08 x = -0.697423831 + -0.08 Combine like terms: -0.697423831 + -0.08 = -0.777423831 x = -0.777423831 Simplifying x = -0.777423831Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.617423831, -0.777423831}
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