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Simplifying 4.905x2 + 15x + -90 = 0 Reorder the terms: -90 + 15x + 4.905x2 = 0 Solving -90 + 15x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -18.34862385 + 3.058103976x + x2 = 0 Move the constant term to the right: Add '18.34862385' to each side of the equation. -18.34862385 + 3.058103976x + 18.34862385 + x2 = 0 + 18.34862385 Reorder the terms: -18.34862385 + 18.34862385 + 3.058103976x + x2 = 0 + 18.34862385 Combine like terms: -18.34862385 + 18.34862385 = 0.00000000 0.00000000 + 3.058103976x + x2 = 0 + 18.34862385 3.058103976x + x2 = 0 + 18.34862385 Combine like terms: 0 + 18.34862385 = 18.34862385 3.058103976x + x2 = 18.34862385 The x term is 3.058103976x. Take half its coefficient (1.529051988). Square it (2.337999982) and add it to both sides. Add '2.337999982' to each side of the equation. 3.058103976x + 2.337999982 + x2 = 18.34862385 + 2.337999982 Reorder the terms: 2.337999982 + 3.058103976x + x2 = 18.34862385 + 2.337999982 Combine like terms: 18.34862385 + 2.337999982 = 20.686623832 2.337999982 + 3.058103976x + x2 = 20.686623832 Factor a perfect square on the left side: (x + 1.529051988)(x + 1.529051988) = 20.686623832 Calculate the square root of the right side: 4.548255032 Break this problem into two subproblems by setting (x + 1.529051988) equal to 4.548255032 and -4.548255032.Subproblem 1
x + 1.529051988 = 4.548255032 Simplifying x + 1.529051988 = 4.548255032 Reorder the terms: 1.529051988 + x = 4.548255032 Solving 1.529051988 + x = 4.548255032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.529051988' to each side of the equation. 1.529051988 + -1.529051988 + x = 4.548255032 + -1.529051988 Combine like terms: 1.529051988 + -1.529051988 = 0.000000000 0.000000000 + x = 4.548255032 + -1.529051988 x = 4.548255032 + -1.529051988 Combine like terms: 4.548255032 + -1.529051988 = 3.019203044 x = 3.019203044 Simplifying x = 3.019203044Subproblem 2
x + 1.529051988 = -4.548255032 Simplifying x + 1.529051988 = -4.548255032 Reorder the terms: 1.529051988 + x = -4.548255032 Solving 1.529051988 + x = -4.548255032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.529051988' to each side of the equation. 1.529051988 + -1.529051988 + x = -4.548255032 + -1.529051988 Combine like terms: 1.529051988 + -1.529051988 = 0.000000000 0.000000000 + x = -4.548255032 + -1.529051988 x = -4.548255032 + -1.529051988 Combine like terms: -4.548255032 + -1.529051988 = -6.07730702 x = -6.07730702 Simplifying x = -6.07730702Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.019203044, -6.07730702}
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