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Simplifying 4x2 + -24x + 25 = 0 Reorder the terms: 25 + -24x + 4x2 = 0 Solving 25 + -24x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -6x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -6x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -6x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -6x + x2 = 0 + -6.25 -6x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -6x + x2 = -6.25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -6.25 + 9 Reorder the terms: 9 + -6x + x2 = -6.25 + 9 Combine like terms: -6.25 + 9 = 2.75 9 + -6x + x2 = 2.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -3) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -3 = 1.658312395 Simplifying x + -3 = 1.658312395 Reorder the terms: -3 + x = 1.658312395 Solving -3 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.658312395 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.658312395 + 3 x = 1.658312395 + 3 Combine like terms: 1.658312395 + 3 = 4.658312395 x = 4.658312395 Simplifying x = 4.658312395Subproblem 2
x + -3 = -1.658312395 Simplifying x + -3 = -1.658312395 Reorder the terms: -3 + x = -1.658312395 Solving -3 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.658312395 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.658312395 + 3 x = -1.658312395 + 3 Combine like terms: -1.658312395 + 3 = 1.341687605 x = 1.341687605 Simplifying x = 1.341687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.658312395, 1.341687605}
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