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Simplifying -42x2 + 100x + 50 = 0 Reorder the terms: 50 + 100x + -42x2 = 0 Solving 50 + 100x + -42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 50x + -21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 50x + -21x2)' equal to zero and attempt to solve: Simplifying 25 + 50x + -21x2 = 0 Solving 25 + 50x + -21x2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -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 = 2.607709751 1.417233561 + -2.380952381x + x2 = 2.607709751 Factor a perfect square on the left side: (x + -1.190476191)(x + -1.190476191) = 2.607709751 Calculate the square root of the right side: 1.614840472 Break this problem into two subproblems by setting (x + -1.190476191) equal to 1.614840472 and -1.614840472.Subproblem 1
x + -1.190476191 = 1.614840472 Simplifying x + -1.190476191 = 1.614840472 Reorder the terms: -1.190476191 + x = 1.614840472 Solving -1.190476191 + x = 1.614840472 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 = 1.614840472 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = 1.614840472 + 1.190476191 x = 1.614840472 + 1.190476191 Combine like terms: 1.614840472 + 1.190476191 = 2.805316663 x = 2.805316663 Simplifying x = 2.805316663Subproblem 2
x + -1.190476191 = -1.614840472 Simplifying x + -1.190476191 = -1.614840472 Reorder the terms: -1.190476191 + x = -1.614840472 Solving -1.190476191 + x = -1.614840472 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 = -1.614840472 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = -1.614840472 + 1.190476191 x = -1.614840472 + 1.190476191 Combine like terms: -1.614840472 + 1.190476191 = -0.424364281 x = -0.424364281 Simplifying x = -0.424364281Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.805316663, -0.424364281}Solution
x = {2.805316663, -0.424364281}
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