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Simplifying -7 + -18x + 19x2 = 0 Solving -7 + -18x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.3684210526 + -0.9473684211x + x2 = 0 Move the constant term to the right: Add '0.3684210526' to each side of the equation. -0.3684210526 + -0.9473684211x + 0.3684210526 + x2 = 0 + 0.3684210526 Reorder the terms: -0.3684210526 + 0.3684210526 + -0.9473684211x + x2 = 0 + 0.3684210526 Combine like terms: -0.3684210526 + 0.3684210526 = 0.0000000000 0.0000000000 + -0.9473684211x + x2 = 0 + 0.3684210526 -0.9473684211x + x2 = 0 + 0.3684210526 Combine like terms: 0 + 0.3684210526 = 0.3684210526 -0.9473684211x + x2 = 0.3684210526 The x term is -0.9473684211x. Take half its coefficient (-0.4736842106). Square it (0.2243767314) and add it to both sides. Add '0.2243767314' to each side of the equation. -0.9473684211x + 0.2243767314 + x2 = 0.3684210526 + 0.2243767314 Reorder the terms: 0.2243767314 + -0.9473684211x + x2 = 0.3684210526 + 0.2243767314 Combine like terms: 0.3684210526 + 0.2243767314 = 0.592797784 0.2243767314 + -0.9473684211x + x2 = 0.592797784 Factor a perfect square on the left side: (x + -0.4736842106)(x + -0.4736842106) = 0.592797784 Calculate the square root of the right side: 0.769933623 Break this problem into two subproblems by setting (x + -0.4736842106) equal to 0.769933623 and -0.769933623.Subproblem 1
x + -0.4736842106 = 0.769933623 Simplifying x + -0.4736842106 = 0.769933623 Reorder the terms: -0.4736842106 + x = 0.769933623 Solving -0.4736842106 + x = 0.769933623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4736842106' to each side of the equation. -0.4736842106 + 0.4736842106 + x = 0.769933623 + 0.4736842106 Combine like terms: -0.4736842106 + 0.4736842106 = 0.0000000000 0.0000000000 + x = 0.769933623 + 0.4736842106 x = 0.769933623 + 0.4736842106 Combine like terms: 0.769933623 + 0.4736842106 = 1.2436178336 x = 1.2436178336 Simplifying x = 1.2436178336Subproblem 2
x + -0.4736842106 = -0.769933623 Simplifying x + -0.4736842106 = -0.769933623 Reorder the terms: -0.4736842106 + x = -0.769933623 Solving -0.4736842106 + x = -0.769933623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4736842106' to each side of the equation. -0.4736842106 + 0.4736842106 + x = -0.769933623 + 0.4736842106 Combine like terms: -0.4736842106 + 0.4736842106 = 0.0000000000 0.0000000000 + x = -0.769933623 + 0.4736842106 x = -0.769933623 + 0.4736842106 Combine like terms: -0.769933623 + 0.4736842106 = -0.2962494124 x = -0.2962494124 Simplifying x = -0.2962494124Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2436178336, -0.2962494124}
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