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Simplifying 2x2 + 19 = 14x Reorder the terms: 19 + 2x2 = 14x Solving 19 + 2x2 = 14x Solving for variable 'x'. Reorder the terms: 19 + -14x + 2x2 = 14x + -14x Combine like terms: 14x + -14x = 0 19 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + -7x + x2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -7x + -9.5 + x2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -7x + x2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -7x + x2 = 0 + -9.5 -7x + x2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -7x + x2 = -9.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -9.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -9.5 + 12.25 Combine like terms: -9.5 + 12.25 = 2.75 12.25 + -7x + x2 = 2.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -3.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -3.5 = 1.658312395 Simplifying x + -3.5 = 1.658312395 Reorder the terms: -3.5 + x = 1.658312395 Solving -3.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.658312395 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.658312395 + 3.5 x = 1.658312395 + 3.5 Combine like terms: 1.658312395 + 3.5 = 5.158312395 x = 5.158312395 Simplifying x = 5.158312395Subproblem 2
x + -3.5 = -1.658312395 Simplifying x + -3.5 = -1.658312395 Reorder the terms: -3.5 + x = -1.658312395 Solving -3.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.658312395 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.658312395 + 3.5 x = -1.658312395 + 3.5 Combine like terms: -1.658312395 + 3.5 = 1.841687605 x = 1.841687605 Simplifying x = 1.841687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.158312395, 1.841687605}
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