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Simplifying -4x2 + 19x = -320 Reorder the terms: 19x + -4x2 = -320 Solving 19x + -4x2 = -320 Solving for variable 'x'. Reorder the terms: 320 + 19x + -4x2 = -320 + 320 Combine like terms: -320 + 320 = 0 320 + 19x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -80 + -4.75x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -4.75x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -4.75x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -4.75x + x2 = 0 + 80 -4.75x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -4.75x + x2 = 80 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 80 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 80 + 5.640625 Combine like terms: 80 + 5.640625 = 85.640625 5.640625 + -4.75x + x2 = 85.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 85.640625 Calculate the square root of the right side: 9.254222009 Break this problem into two subproblems by setting (x + -2.375) equal to 9.254222009 and -9.254222009.Subproblem 1
x + -2.375 = 9.254222009 Simplifying x + -2.375 = 9.254222009 Reorder the terms: -2.375 + x = 9.254222009 Solving -2.375 + x = 9.254222009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 9.254222009 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 9.254222009 + 2.375 x = 9.254222009 + 2.375 Combine like terms: 9.254222009 + 2.375 = 11.629222009 x = 11.629222009 Simplifying x = 11.629222009Subproblem 2
x + -2.375 = -9.254222009 Simplifying x + -2.375 = -9.254222009 Reorder the terms: -2.375 + x = -9.254222009 Solving -2.375 + x = -9.254222009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -9.254222009 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -9.254222009 + 2.375 x = -9.254222009 + 2.375 Combine like terms: -9.254222009 + 2.375 = -6.879222009 x = -6.879222009 Simplifying x = -6.879222009Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.629222009, -6.879222009}
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