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Simplifying 2(63x2 + -15x + -10) = 0 Reorder the terms: 2(-10 + -15x + 63x2) = 0 (-10 * 2 + -15x * 2 + 63x2 * 2) = 0 (-20 + -30x + 126x2) = 0 Solving -20 + -30x + 126x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -15x + 63x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -15x + 63x2)' equal to zero and attempt to solve: Simplifying -10 + -15x + 63x2 = 0 Solving -10 + -15x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.1587301587 + -0.2380952381x + x2 = 0 Move the constant term to the right: Add '0.1587301587' to each side of the equation. -0.1587301587 + -0.2380952381x + 0.1587301587 + x2 = 0 + 0.1587301587 Reorder the terms: -0.1587301587 + 0.1587301587 + -0.2380952381x + x2 = 0 + 0.1587301587 Combine like terms: -0.1587301587 + 0.1587301587 = 0.0000000000 0.0000000000 + -0.2380952381x + x2 = 0 + 0.1587301587 -0.2380952381x + x2 = 0 + 0.1587301587 Combine like terms: 0 + 0.1587301587 = 0.1587301587 -0.2380952381x + x2 = 0.1587301587 The x term is -0.2380952381x. Take half its coefficient (-0.1190476191). Square it (0.01417233561) and add it to both sides. Add '0.01417233561' to each side of the equation. -0.2380952381x + 0.01417233561 + x2 = 0.1587301587 + 0.01417233561 Reorder the terms: 0.01417233561 + -0.2380952381x + x2 = 0.1587301587 + 0.01417233561 Combine like terms: 0.1587301587 + 0.01417233561 = 0.17290249431 0.01417233561 + -0.2380952381x + x2 = 0.17290249431 Factor a perfect square on the left side: (x + -0.1190476191)(x + -0.1190476191) = 0.17290249431 Calculate the square root of the right side: 0.415815457 Break this problem into two subproblems by setting (x + -0.1190476191) equal to 0.415815457 and -0.415815457.Subproblem 1
x + -0.1190476191 = 0.415815457 Simplifying x + -0.1190476191 = 0.415815457 Reorder the terms: -0.1190476191 + x = 0.415815457 Solving -0.1190476191 + x = 0.415815457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1190476191' to each side of the equation. -0.1190476191 + 0.1190476191 + x = 0.415815457 + 0.1190476191 Combine like terms: -0.1190476191 + 0.1190476191 = 0.0000000000 0.0000000000 + x = 0.415815457 + 0.1190476191 x = 0.415815457 + 0.1190476191 Combine like terms: 0.415815457 + 0.1190476191 = 0.5348630761 x = 0.5348630761 Simplifying x = 0.5348630761Subproblem 2
x + -0.1190476191 = -0.415815457 Simplifying x + -0.1190476191 = -0.415815457 Reorder the terms: -0.1190476191 + x = -0.415815457 Solving -0.1190476191 + x = -0.415815457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1190476191' to each side of the equation. -0.1190476191 + 0.1190476191 + x = -0.415815457 + 0.1190476191 Combine like terms: -0.1190476191 + 0.1190476191 = 0.0000000000 0.0000000000 + x = -0.415815457 + 0.1190476191 x = -0.415815457 + 0.1190476191 Combine like terms: -0.415815457 + 0.1190476191 = -0.2967678379 x = -0.2967678379 Simplifying x = -0.2967678379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5348630761, -0.2967678379}Solution
x = {0.5348630761, -0.2967678379}
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