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Simplifying -25x2 + 15x + 225 = 0 Reorder the terms: 225 + 15x + -25x2 = 0 Solving 225 + 15x + -25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(45 + 3x + -5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(45 + 3x + -5x2)' equal to zero and attempt to solve: Simplifying 45 + 3x + -5x2 = 0 Solving 45 + 3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9 + -0.6x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.6x + x2 = 0 + 9 -0.6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.6x + x2 = 9 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 9 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 9 + 0.09 Combine like terms: 9 + 0.09 = 9.09 0.09 + -0.6x + x2 = 9.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 9.09 Calculate the square root of the right side: 3.014962686 Break this problem into two subproblems by setting (x + -0.3) equal to 3.014962686 and -3.014962686.Subproblem 1
x + -0.3 = 3.014962686 Simplifying x + -0.3 = 3.014962686 Reorder the terms: -0.3 + x = 3.014962686 Solving -0.3 + x = 3.014962686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 3.014962686 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 3.014962686 + 0.3 x = 3.014962686 + 0.3 Combine like terms: 3.014962686 + 0.3 = 3.314962686 x = 3.314962686 Simplifying x = 3.314962686Subproblem 2
x + -0.3 = -3.014962686 Simplifying x + -0.3 = -3.014962686 Reorder the terms: -0.3 + x = -3.014962686 Solving -0.3 + x = -3.014962686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -3.014962686 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -3.014962686 + 0.3 x = -3.014962686 + 0.3 Combine like terms: -3.014962686 + 0.3 = -2.714962686 x = -2.714962686 Simplifying x = -2.714962686Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.314962686, -2.714962686}Solution
x = {3.314962686, -2.714962686}
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