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Simplifying -7x2 + 36x + 17x2 + -21 = 0 Reorder the terms: -21 + 36x + -7x2 + 17x2 = 0 Combine like terms: -7x2 + 17x2 = 10x2 -21 + 36x + 10x2 = 0 Solving -21 + 36x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + 3.6x + x2 = 0.0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 3.6x + 2.1 + x2 = 0.0 + 2.1 Reorder the terms: -2.1 + 2.1 + 3.6x + x2 = 0.0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 3.6x + x2 = 0.0 + 2.1 3.6x + x2 = 0.0 + 2.1 Combine like terms: 0.0 + 2.1 = 2.1 3.6x + x2 = 2.1 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 2.1 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 2.1 + 3.24 Combine like terms: 2.1 + 3.24 = 5.34 3.24 + 3.6x + x2 = 5.34 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 5.34 Calculate the square root of the right side: 2.310844002 Break this problem into two subproblems by setting (x + 1.8) equal to 2.310844002 and -2.310844002.Subproblem 1
x + 1.8 = 2.310844002 Simplifying x + 1.8 = 2.310844002 Reorder the terms: 1.8 + x = 2.310844002 Solving 1.8 + x = 2.310844002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.310844002 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.310844002 + -1.8 x = 2.310844002 + -1.8 Combine like terms: 2.310844002 + -1.8 = 0.510844002 x = 0.510844002 Simplifying x = 0.510844002Subproblem 2
x + 1.8 = -2.310844002 Simplifying x + 1.8 = -2.310844002 Reorder the terms: 1.8 + x = -2.310844002 Solving 1.8 + x = -2.310844002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.310844002 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.310844002 + -1.8 x = -2.310844002 + -1.8 Combine like terms: -2.310844002 + -1.8 = -4.110844002 x = -4.110844002 Simplifying x = -4.110844002Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.510844002, -4.110844002}
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