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Simplifying -24x2 + -50x + 30 = 0 Reorder the terms: 30 + -50x + -24x2 = 0 Solving 30 + -50x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -25x + -12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -25x + -12x2)' equal to zero and attempt to solve: Simplifying 15 + -25x + -12x2 = 0 Solving 15 + -25x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.25 + 2.083333333x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.083333333x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.083333333x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.083333333x + x2 = 0 + 1.25 2.083333333x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.083333333x + x2 = 1.25 The x term is 2.083333333x. Take half its coefficient (1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. 2.083333333x + 1.085069445 + x2 = 1.25 + 1.085069445 Reorder the terms: 1.085069445 + 2.083333333x + x2 = 1.25 + 1.085069445 Combine like terms: 1.25 + 1.085069445 = 2.335069445 1.085069445 + 2.083333333x + x2 = 2.335069445 Factor a perfect square on the left side: (x + 1.041666667)(x + 1.041666667) = 2.335069445 Calculate the square root of the right side: 1.528093402 Break this problem into two subproblems by setting (x + 1.041666667) equal to 1.528093402 and -1.528093402.Subproblem 1
x + 1.041666667 = 1.528093402 Simplifying x + 1.041666667 = 1.528093402 Reorder the terms: 1.041666667 + x = 1.528093402 Solving 1.041666667 + x = 1.528093402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = 1.528093402 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = 1.528093402 + -1.041666667 x = 1.528093402 + -1.041666667 Combine like terms: 1.528093402 + -1.041666667 = 0.486426735 x = 0.486426735 Simplifying x = 0.486426735Subproblem 2
x + 1.041666667 = -1.528093402 Simplifying x + 1.041666667 = -1.528093402 Reorder the terms: 1.041666667 + x = -1.528093402 Solving 1.041666667 + x = -1.528093402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = -1.528093402 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = -1.528093402 + -1.041666667 x = -1.528093402 + -1.041666667 Combine like terms: -1.528093402 + -1.041666667 = -2.569760069 x = -2.569760069 Simplifying x = -2.569760069Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.486426735, -2.569760069}Solution
x = {0.486426735, -2.569760069}
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