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Simplifying 2(25x2 + -30x + 9) = 7 Reorder the terms: 2(9 + -30x + 25x2) = 7 (9 * 2 + -30x * 2 + 25x2 * 2) = 7 (18 + -60x + 50x2) = 7 Solving 18 + -60x + 50x2 = 7 Solving for variable 'x'. Reorder the terms: 18 + -7 + -60x + 50x2 = 7 + -7 Combine like terms: 18 + -7 = 11 11 + -60x + 50x2 = 7 + -7 Combine like terms: 7 + -7 = 0 11 + -60x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.22 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '-0.22' to each side of the equation. 0.22 + -1.2x + -0.22 + x2 = 0.0 + -0.22 Reorder the terms: 0.22 + -0.22 + -1.2x + x2 = 0.0 + -0.22 Combine like terms: 0.22 + -0.22 = 0.00 0.00 + -1.2x + x2 = 0.0 + -0.22 -1.2x + x2 = 0.0 + -0.22 Combine like terms: 0.0 + -0.22 = -0.22 -1.2x + x2 = -0.22 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.22 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.22 + 0.36 Combine like terms: -0.22 + 0.36 = 0.14 0.36 + -1.2x + x2 = 0.14 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.14 Calculate the square root of the right side: 0.374165739 Break this problem into two subproblems by setting (x + -0.6) equal to 0.374165739 and -0.374165739.Subproblem 1
x + -0.6 = 0.374165739 Simplifying x + -0.6 = 0.374165739 Reorder the terms: -0.6 + x = 0.374165739 Solving -0.6 + x = 0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.374165739 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.374165739 + 0.6 x = 0.374165739 + 0.6 Combine like terms: 0.374165739 + 0.6 = 0.974165739 x = 0.974165739 Simplifying x = 0.974165739Subproblem 2
x + -0.6 = -0.374165739 Simplifying x + -0.6 = -0.374165739 Reorder the terms: -0.6 + x = -0.374165739 Solving -0.6 + x = -0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.374165739 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.374165739 + 0.6 x = -0.374165739 + 0.6 Combine like terms: -0.374165739 + 0.6 = 0.225834261 x = 0.225834261 Simplifying x = 0.225834261Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.974165739, 0.225834261}
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