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Simplifying 130x + -4x2 + 425 = 0 Reorder the terms: 425 + 130x + -4x2 = 0 Solving 425 + 130x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -106.25 + -32.5x + x2 = 0 Move the constant term to the right: Add '106.25' to each side of the equation. -106.25 + -32.5x + 106.25 + x2 = 0 + 106.25 Reorder the terms: -106.25 + 106.25 + -32.5x + x2 = 0 + 106.25 Combine like terms: -106.25 + 106.25 = 0.00 0.00 + -32.5x + x2 = 0 + 106.25 -32.5x + x2 = 0 + 106.25 Combine like terms: 0 + 106.25 = 106.25 -32.5x + x2 = 106.25 The x term is -32.5x. Take half its coefficient (-16.25). Square it (264.0625) and add it to both sides. Add '264.0625' to each side of the equation. -32.5x + 264.0625 + x2 = 106.25 + 264.0625 Reorder the terms: 264.0625 + -32.5x + x2 = 106.25 + 264.0625 Combine like terms: 106.25 + 264.0625 = 370.3125 264.0625 + -32.5x + x2 = 370.3125 Factor a perfect square on the left side: (x + -16.25)(x + -16.25) = 370.3125 Calculate the square root of the right side: 19.243505398 Break this problem into two subproblems by setting (x + -16.25) equal to 19.243505398 and -19.243505398.Subproblem 1
x + -16.25 = 19.243505398 Simplifying x + -16.25 = 19.243505398 Reorder the terms: -16.25 + x = 19.243505398 Solving -16.25 + x = 19.243505398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = 19.243505398 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = 19.243505398 + 16.25 x = 19.243505398 + 16.25 Combine like terms: 19.243505398 + 16.25 = 35.493505398 x = 35.493505398 Simplifying x = 35.493505398Subproblem 2
x + -16.25 = -19.243505398 Simplifying x + -16.25 = -19.243505398 Reorder the terms: -16.25 + x = -19.243505398 Solving -16.25 + x = -19.243505398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = -19.243505398 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = -19.243505398 + 16.25 x = -19.243505398 + 16.25 Combine like terms: -19.243505398 + 16.25 = -2.993505398 x = -2.993505398 Simplifying x = -2.993505398Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.493505398, -2.993505398}
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