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Simplifying 5(x2 + -9x) + -2(3x + 4) + 7 = 0 Reorder the terms: 5(-9x + x2) + -2(3x + 4) + 7 = 0 (-9x * 5 + x2 * 5) + -2(3x + 4) + 7 = 0 (-45x + 5x2) + -2(3x + 4) + 7 = 0 Reorder the terms: -45x + 5x2 + -2(4 + 3x) + 7 = 0 -45x + 5x2 + (4 * -2 + 3x * -2) + 7 = 0 -45x + 5x2 + (-8 + -6x) + 7 = 0 Reorder the terms: -8 + 7 + -45x + -6x + 5x2 = 0 Combine like terms: -8 + 7 = -1 -1 + -45x + -6x + 5x2 = 0 Combine like terms: -45x + -6x = -51x -1 + -51x + 5x2 = 0 Solving -1 + -51x + 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'. -0.2 + -10.2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -10.2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -10.2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -10.2x + x2 = 0 + 0.2 -10.2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -10.2x + x2 = 0.2 The x term is -10.2x. Take half its coefficient (-5.1). Square it (26.01) and add it to both sides. Add '26.01' to each side of the equation. -10.2x + 26.01 + x2 = 0.2 + 26.01 Reorder the terms: 26.01 + -10.2x + x2 = 0.2 + 26.01 Combine like terms: 0.2 + 26.01 = 26.21 26.01 + -10.2x + x2 = 26.21 Factor a perfect square on the left side: (x + -5.1)(x + -5.1) = 26.21 Calculate the square root of the right side: 5.119570294 Break this problem into two subproblems by setting (x + -5.1) equal to 5.119570294 and -5.119570294.Subproblem 1
x + -5.1 = 5.119570294 Simplifying x + -5.1 = 5.119570294 Reorder the terms: -5.1 + x = 5.119570294 Solving -5.1 + x = 5.119570294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = 5.119570294 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = 5.119570294 + 5.1 x = 5.119570294 + 5.1 Combine like terms: 5.119570294 + 5.1 = 10.219570294 x = 10.219570294 Simplifying x = 10.219570294Subproblem 2
x + -5.1 = -5.119570294 Simplifying x + -5.1 = -5.119570294 Reorder the terms: -5.1 + x = -5.119570294 Solving -5.1 + x = -5.119570294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = -5.119570294 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = -5.119570294 + 5.1 x = -5.119570294 + 5.1 Combine like terms: -5.119570294 + 5.1 = -0.019570294 x = -0.019570294 Simplifying x = -0.019570294Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.219570294, -0.019570294}
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