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Simplifying 5.25x2 + -12.5x + 6.25 = 0 Reorder the terms: 6.25 + -12.5x + 5.25x2 = 0 Solving 6.25 + -12.5x + 5.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.25 the coefficient of the squared term: Divide each side by '5.25'. 1.19047619 + -2.380952381x + x2 = 0 Move the constant term to the right: Add '-1.19047619' to each side of the equation. 1.19047619 + -2.380952381x + -1.19047619 + x2 = 0 + -1.19047619 Reorder the terms: 1.19047619 + -1.19047619 + -2.380952381x + x2 = 0 + -1.19047619 Combine like terms: 1.19047619 + -1.19047619 = 0.00000000 0.00000000 + -2.380952381x + x2 = 0 + -1.19047619 -2.380952381x + x2 = 0 + -1.19047619 Combine like terms: 0 + -1.19047619 = -1.19047619 -2.380952381x + x2 = -1.19047619 The x term is -2.380952381x. Take half its coefficient (-1.190476191). Square it (1.417233561) and add it to both sides. Add '1.417233561' to each side of the equation. -2.380952381x + 1.417233561 + x2 = -1.19047619 + 1.417233561 Reorder the terms: 1.417233561 + -2.380952381x + x2 = -1.19047619 + 1.417233561 Combine like terms: -1.19047619 + 1.417233561 = 0.226757371 1.417233561 + -2.380952381x + x2 = 0.226757371 Factor a perfect square on the left side: (x + -1.190476191)(x + -1.190476191) = 0.226757371 Calculate the square root of the right side: 0.476190478 Break this problem into two subproblems by setting (x + -1.190476191) equal to 0.476190478 and -0.476190478.Subproblem 1
x + -1.190476191 = 0.476190478 Simplifying x + -1.190476191 = 0.476190478 Reorder the terms: -1.190476191 + x = 0.476190478 Solving -1.190476191 + x = 0.476190478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.190476191' to each side of the equation. -1.190476191 + 1.190476191 + x = 0.476190478 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = 0.476190478 + 1.190476191 x = 0.476190478 + 1.190476191 Combine like terms: 0.476190478 + 1.190476191 = 1.666666669 x = 1.666666669 Simplifying x = 1.666666669Subproblem 2
x + -1.190476191 = -0.476190478 Simplifying x + -1.190476191 = -0.476190478 Reorder the terms: -1.190476191 + x = -0.476190478 Solving -1.190476191 + x = -0.476190478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.190476191' to each side of the equation. -1.190476191 + 1.190476191 + x = -0.476190478 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = -0.476190478 + 1.190476191 x = -0.476190478 + 1.190476191 Combine like terms: -0.476190478 + 1.190476191 = 0.714285713 x = 0.714285713 Simplifying x = 0.714285713Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.666666669, 0.714285713}
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