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Simplifying -5x2 + 45x + 25 = 0 Reorder the terms: 25 + 45x + -5x2 = 0 Solving 25 + 45x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + 9x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + 9x + -1x2 = 0 Solving 5 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -9x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -9x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -9x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9x + x2 = 0 + 5 -9x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -9x + x2 = 5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 5 + 20.25 Combine like terms: 5 + 20.25 = 25.25 20.25 + -9x + x2 = 25.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -4.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -4.5 = 5.024937811 Simplifying x + -4.5 = 5.024937811 Reorder the terms: -4.5 + x = 5.024937811 Solving -4.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.024937811 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.024937811 + 4.5 x = 5.024937811 + 4.5 Combine like terms: 5.024937811 + 4.5 = 9.524937811 x = 9.524937811 Simplifying x = 9.524937811Subproblem 2
x + -4.5 = -5.024937811 Simplifying x + -4.5 = -5.024937811 Reorder the terms: -4.5 + x = -5.024937811 Solving -4.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.024937811 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.024937811 + 4.5 x = -5.024937811 + 4.5 Combine like terms: -5.024937811 + 4.5 = -0.524937811 x = -0.524937811 Simplifying x = -0.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.524937811, -0.524937811}Solution
x = {9.524937811, -0.524937811}
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