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Simplifying -15x2 + -44x + 21 = 0 Reorder the terms: 21 + -44x + -15x2 = 0 Solving 21 + -44x + -15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -1.4 + 2.933333333x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2.933333333x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2.933333333x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2.933333333x + x2 = 0 + 1.4 2.933333333x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2.933333333x + x2 = 1.4 The x term is 2.933333333x. Take half its coefficient (1.466666667). Square it (2.151111112) and add it to both sides. Add '2.151111112' to each side of the equation. 2.933333333x + 2.151111112 + x2 = 1.4 + 2.151111112 Reorder the terms: 2.151111112 + 2.933333333x + x2 = 1.4 + 2.151111112 Combine like terms: 1.4 + 2.151111112 = 3.551111112 2.151111112 + 2.933333333x + x2 = 3.551111112 Factor a perfect square on the left side: (x + 1.466666667)(x + 1.466666667) = 3.551111112 Calculate the square root of the right side: 1.884439204 Break this problem into two subproblems by setting (x + 1.466666667) equal to 1.884439204 and -1.884439204.Subproblem 1
x + 1.466666667 = 1.884439204 Simplifying x + 1.466666667 = 1.884439204 Reorder the terms: 1.466666667 + x = 1.884439204 Solving 1.466666667 + x = 1.884439204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.466666667' to each side of the equation. 1.466666667 + -1.466666667 + x = 1.884439204 + -1.466666667 Combine like terms: 1.466666667 + -1.466666667 = 0.000000000 0.000000000 + x = 1.884439204 + -1.466666667 x = 1.884439204 + -1.466666667 Combine like terms: 1.884439204 + -1.466666667 = 0.417772537 x = 0.417772537 Simplifying x = 0.417772537Subproblem 2
x + 1.466666667 = -1.884439204 Simplifying x + 1.466666667 = -1.884439204 Reorder the terms: 1.466666667 + x = -1.884439204 Solving 1.466666667 + x = -1.884439204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.466666667' to each side of the equation. 1.466666667 + -1.466666667 + x = -1.884439204 + -1.466666667 Combine like terms: 1.466666667 + -1.466666667 = 0.000000000 0.000000000 + x = -1.884439204 + -1.466666667 x = -1.884439204 + -1.466666667 Combine like terms: -1.884439204 + -1.466666667 = -3.351105871 x = -3.351105871 Simplifying x = -3.351105871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.417772537, -3.351105871}
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