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Simplifying 25x2 + -6x + -4 = 0 Reorder the terms: -4 + -6x + 25x2 = 0 Solving -4 + -6x + 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'. -0.16 + -0.24x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.24x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.24x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.24x + x2 = 0 + 0.16 -0.24x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.24x + x2 = 0.16 The x term is -0.24x. Take half its coefficient (-0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. -0.24x + 0.0144 + x2 = 0.16 + 0.0144 Reorder the terms: 0.0144 + -0.24x + x2 = 0.16 + 0.0144 Combine like terms: 0.16 + 0.0144 = 0.1744 0.0144 + -0.24x + x2 = 0.1744 Factor a perfect square on the left side: (x + -0.12)(x + -0.12) = 0.1744 Calculate the square root of the right side: 0.41761226 Break this problem into two subproblems by setting (x + -0.12) equal to 0.41761226 and -0.41761226.Subproblem 1
x + -0.12 = 0.41761226 Simplifying x + -0.12 = 0.41761226 Reorder the terms: -0.12 + x = 0.41761226 Solving -0.12 + x = 0.41761226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = 0.41761226 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = 0.41761226 + 0.12 x = 0.41761226 + 0.12 Combine like terms: 0.41761226 + 0.12 = 0.53761226 x = 0.53761226 Simplifying x = 0.53761226Subproblem 2
x + -0.12 = -0.41761226 Simplifying x + -0.12 = -0.41761226 Reorder the terms: -0.12 + x = -0.41761226 Solving -0.12 + x = -0.41761226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = -0.41761226 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = -0.41761226 + 0.12 x = -0.41761226 + 0.12 Combine like terms: -0.41761226 + 0.12 = -0.29761226 x = -0.29761226 Simplifying x = -0.29761226Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.53761226, -0.29761226}
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