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Simplifying (3x2 + 7x + 5) + (2x2 + 9x) = 0 Reorder the terms: (5 + 7x + 3x2) + (2x2 + 9x) = 0 Remove parenthesis around (5 + 7x + 3x2) 5 + 7x + 3x2 + (2x2 + 9x) = 0 Reorder the terms: 5 + 7x + 3x2 + (9x + 2x2) = 0 Remove parenthesis around (9x + 2x2) 5 + 7x + 3x2 + 9x + 2x2 = 0 Reorder the terms: 5 + 7x + 9x + 3x2 + 2x2 = 0 Combine like terms: 7x + 9x = 16x 5 + 16x + 3x2 + 2x2 = 0 Combine like terms: 3x2 + 2x2 = 5x2 5 + 16x + 5x2 = 0 Solving 5 + 16x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 3.2x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.2x + x2 = 0 + -1 3.2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.2x + x2 = -1 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -1 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -1 + 2.56 Combine like terms: -1 + 2.56 = 1.56 2.56 + 3.2x + x2 = 1.56 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (x + 1.6) equal to 1.2489996 and -1.2489996.Subproblem 1
x + 1.6 = 1.2489996 Simplifying x + 1.6 = 1.2489996 Reorder the terms: 1.6 + x = 1.2489996 Solving 1.6 + x = 1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.2489996 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.2489996 + -1.6 x = 1.2489996 + -1.6 Combine like terms: 1.2489996 + -1.6 = -0.3510004 x = -0.3510004 Simplifying x = -0.3510004Subproblem 2
x + 1.6 = -1.2489996 Simplifying x + 1.6 = -1.2489996 Reorder the terms: 1.6 + x = -1.2489996 Solving 1.6 + x = -1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.2489996 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.2489996 + -1.6 x = -1.2489996 + -1.6 Combine like terms: -1.2489996 + -1.6 = -2.8489996 x = -2.8489996 Simplifying x = -2.8489996Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3510004, -2.8489996}
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