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Simplifying 4x2 + -17x + -15 = 30 Reorder the terms: -15 + -17x + 4x2 = 30 Solving -15 + -17x + 4x2 = 30 Solving for variable 'x'. Reorder the terms: -15 + -30 + -17x + 4x2 = 30 + -30 Combine like terms: -15 + -30 = -45 -45 + -17x + 4x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -45 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -4.25x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -4.25x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -4.25x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -4.25x + x2 = 0 + 11.25 -4.25x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -4.25x + x2 = 11.25 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 11.25 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 11.25 + 4.515625 Combine like terms: 11.25 + 4.515625 = 15.765625 4.515625 + -4.25x + x2 = 15.765625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 15.765625 Calculate the square root of the right side: 3.970595044 Break this problem into two subproblems by setting (x + -2.125) equal to 3.970595044 and -3.970595044.Subproblem 1
x + -2.125 = 3.970595044 Simplifying x + -2.125 = 3.970595044 Reorder the terms: -2.125 + x = 3.970595044 Solving -2.125 + x = 3.970595044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 3.970595044 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 3.970595044 + 2.125 x = 3.970595044 + 2.125 Combine like terms: 3.970595044 + 2.125 = 6.095595044 x = 6.095595044 Simplifying x = 6.095595044Subproblem 2
x + -2.125 = -3.970595044 Simplifying x + -2.125 = -3.970595044 Reorder the terms: -2.125 + x = -3.970595044 Solving -2.125 + x = -3.970595044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -3.970595044 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -3.970595044 + 2.125 x = -3.970595044 + 2.125 Combine like terms: -3.970595044 + 2.125 = -1.845595044 x = -1.845595044 Simplifying x = -1.845595044Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.095595044, -1.845595044}
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